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In this work, a numerical study on molecular beam scattering of a nitrogen molecule from a graphite surface has been performed. The study was carried out using the molecular dynamics method. The focus of the study is mainly placed on investigating the scattering dynamics in the case of strong rotational non-equilibrium, defined here as a state in which rotational temperature of a molecule strongly deviates from the room temperature. To that end, the incident beam velocity and initial rotational energy of nitrogen molecules have been varied greatly in order to capture a broad range of possible initial states. The obtained results provide valuable insight into the nature of energy transfer occurring during collisions and help to quantify the intensity of rotational–translational coupling between inner kinetic modes in gas–surface collisions. Consequently, the collected data can potentially be used for more accurate characterization of the respective phenomena and improve the quality of boundary models used in rarefied gas flow simulations. [ABSTRACT FROM AUTHOR]

In this work, a gas separation approach based on the selective rotational excitation of different species is investigated. The presented method is particularly suitable for separating gases of similar or equal masses, such as isotopes and isomers. The selective rotational excitation is achieved by a targeted application of multiple non-resonant ultrashort laser pulses. Upon collision with a solid surface, a part of the excited rotational energy gets transferred into translational energy. By creating a discernible difference in average thermal velocities between the species of similar masses, an increased diffusivity of the excited species can be utilized for its successful separation. In order to test the validity of the novel separation technique, a comprehensive computational framework was developed. The energy transfer in gas–surface collisions was analyzed in great detail using a state-of-the-art molecular dynamics code, and the obtained data offered invaluable insight into the nature of scattering dynamics. Furthermore, a novel data-driven approach to gas–surface interaction modeling based on the recently introduced distribution element tree method was proposed. Relevant numerical and experimental data on the selective rotational excitation were gathered, and they served as an input for the performed numerical simulations. Using the developed computational framework, the validity of the proposed separation scheme was tested on a mixture of two species with identical mass. The obtained data offer numerical evidence supporting the proposed separation concept. [ABSTRACT FROM AUTHOR]

Summary: Fluid injection–induced tensile opening is modeled using an extended finite volume method (XFVM). An embedded fracture strategy is used for the flow problem, that is, the fractures are discretized using finite volume segments without resolving the grid around them. Further, the discontinuities across fractures are modeled using special basis functions. The fracture openings due to enhanced fluid pressure and the associated shear slip due to traction free boundary condition on the fracture segments are both modeled using these special discontinuity basis functions. Mass transfer between fractures and matrix is modeled using the pressure difference. The enhancement of fracture storativity due to tensile opening leads to stronger coupling between flow and mechanics. An iterative scheme relying on the fixed‐stress approach for fractures, which conserves the stress dependent terms over each iteration of the flow problem, has been introduced. Tensile opening has been simulated for single fractures embedded in two‐ and three‐dimensional matrices. The convergence criterion for sequentially implicit fixed‐stress scheme for fractures embedded in elastic media is established and has been validated numerically. Further, for 2D simulations, the effect of the matrix permeability for fracture propagation due to tensile opening has been studied. [ABSTRACT FROM AUTHOR]

In reservoir simulation, it is important to understand the mechanical behaviour of fractured rocks and the effect of shear and tensile displacements of fractures on their aperture. Tensile opening directly enhances the fracture aperture, whereas shear of a preexisting rough-walled fracture creates aperture changes dependent on the local stress state. Since fracture dilatation increases reservoir permeability, both processes must be included in a realistic and consistent manner into the mechanical reservoir simulation model. Here, we use the extended finite volume method (XFVM) to conduct flow and geomechanics simulations. In XFVM, fractures are embedded in a poroelastic matrix and are modelled with discontinuous basis functions. On each fracture segment the tractions and compressive forces are calculated, and one extra degree of freedom is added for both the shear and tensile displacement. In this particular XFVM implementation we assume that linear elasticity and steady state fluid pressure adequately constrain the effective stress. In this paper, shear dilation is not calculated a posteriori, but it enters the equations such that aperture changes directly affect the stress state. This is accomplished by adding shear dilation to the displacement gradients and therefore ascertains a consistent representation in the stress-strain relations and force balances. We illustrate and discuss the influence of this extra term in two simple test cases and in a realistic layer-restricted two-dimensional fracture network subjected to plausible in situ stress and pore pressure conditions. [ABSTRACT FROM AUTHOR]

Buoyant incompressible multiphase flow and transport in porous media typically is simulated by coupling an elliptic flow equation with a hyperbolic transport description. The tight coupling between flow and transport either requires a fully implicit solution algorithm or very small time steps, if solved sequentially. In any case, however, a large linear system has to be solved each time step. Here a new solution approach is devised, which relies on solving a coupled hyperbolic system of conservation laws with an explicit finite volume method. Consequently, only local operations have to be performed, which is a great advantage in case of massive parallel simulations and if GPUs are employed. The devised method is based on the isothermal Euler equations with momentum source terms accounting for resistance due to the porous medium and buoyancy. In this system the pressure is proportional to the density and in case of very small Mach numbers and relative density variation, the computed velocity field is divergence free and converges towards the mean total volumetric flow in the porous domain. To account for saturation transport, the system was augmented by an additional hyperbolic equation. In order to obtain the numerical fluxes, a characteristic based approximative Riemann solver was developed and 2nd order accuracy in space and time is achieved by piecewise linear reconstruction. Two-phase flow test cases with buoyant plumes and a lock exchange problem demonstrate that the devised hyperbolic approach recovers the correct incompressible solutions. Numerical experiments also demonstrate that the method is accurate and efficient. Thus the devised method is very promising, and conceptually it also can be applied for flow and transport in heterogeneous media; but it remains to be investigated how well it performs for such cases. • Flow and transport are described by a coupled hyperbolic system of PDEs. • Fully explicit solution scheme for strongly coupled two-phase flow in porous media. • An efficient approximate Riemann solver for the numerical fluxes is devised. • Second order in space and time is achieved by a TVD method. • The proposed method is an ideal candidate for GPUs. [ABSTRACT FROM AUTHOR]

The Vlasov-Fokker-Planck equation (together with Maxwell's equations) provides the basis for plasma flow calculations. While the terms accounting for long range forces are established, different drift and diffusion terms are used to describe Coulomb collisions. Here, linear drift and a constant diffusion coefficient are considered and the electromagnetic fields are imposed, i.e., plasma frequency is not addressed. The solution algorithm is based on evolving computational particles of a large ensemble according to a Langevin equation, whereas the time step size is typically limited by plasma frequency, Coulomb collision frequency and cyclotron frequency. To overcome the latter two time step size constraints, a novel time integration scheme for the particle evolution is presented. It only requires that gradients of mean velocity, bath temperature, magnetic field and electric field have to be resolved along the trajectories. In fact, if these gradients are zero, then the new integration scheme is statistically exact; no matter how large the time step is chosen. Obviously, this is a computational advantage compared to classical integration schemes, which is demonstrated with numerical experiments of isolated charged particle trajectories under the influence of constant magnetic- and electric fields. Besides single ion trajectories, also plasma flow in spatially varying electromagnetic fields was investigated, that is, the influence of time step size and grid resolution on the final solution was studied. • The research highlight presented in this paper is an analytical solution of the coupled Langevin equations as they result from the Vlasov-Fokker-Planck equation for plasma flow with constant electromagnetic fields and constant friction coefficient. • This analytical solution involves a transformation into complex space and allows to take extremely large time steps when used in a solution algorithm. • This is demonstrated in the paper with numerical studies. [ABSTRACT FROM AUTHOR]

Direct simulation Monte-Carlo (DSMC) is the most established method for rarefied gas flow simulations. It is valid from continuum to near vacuum, but in cases involving small Knudsen numbers (Kn), it suffers from high computational cost. The Fokker-Planck (FP) method, on the other hand, is almost as accurate as DSMC for small to moderate Kn, but it does not have the computational drawback of DSMC, if Kn is small [P. Jenny, M. Torrilhon, and S. Heinz, "A solution algorithm for the fluid dynamic equations based on a stochastic model for molecular motion," J. Comput. Phys. 229, 1077–1098 (2010) and H. Gorji, M. Torrilhon, and P. Jenny, "Fokker–Planck model for computational studies of monatomic rarefied gas flows," J. Fluid Mech. 680, 574–601 (2011)]. Especially attractive is the combination of the two approaches leading to the FP-DSMC method. Opposed to other hybrid methods, e.g., coupled DSMC/Navier-Stokes solvers, it is relatively straightforward to couple DSMC with the FP method since both are based on particle solution algorithms sharing the same data structure and having similar components. Regarding the numerical accuracy of such particle methods, one has to distinguish between spatial truncation errors, time stepping errors, statistical errors and bias errors. In this paper, the bias error of the FP method is analyzed in detail, and it is shown how it can be reduced without increasing the particle number to an exorbitant level. The effectiveness of the discussed bias error reduction scheme is demonstrated for uniform shear flow, for which an analytical reference solution was derived. [ABSTRACT FROM AUTHOR]

This study continues the exploration of temporal large-eddy simulation, particularly the extension of the temporal direct deconvolution method (TDDM) with a regularization term based on spatial dissipation. Furthermore, we aim to put insight stemming from previous work to test. Specifically, the hypothesis is that the temporal residual-stress leads to a reduction of the required artificial dissipation in under-resolved simulations. Moreover, this work seeks corroborate earlier discoveries with a posteriori results. We perform a numerical examination of two different spatial regularization terms in conjunction with TDDM: a spatial variant of selective frequency damping, functioning as a relaxation term that gradually drifts the velocity toward the filtered velocity, and the dynamic Smagorinsky model incorporating a prefactor. We test various cases, including the Taylor–Green vortex flow with a Reynolds number of Re = 3000, forced homogeneous isotropic turbulence with R e λ = 200 , turbulent channel flow at R e τ = 590 , and the flow over a periodic hill with Re = 10 935. Additionally, we also analyze the various dissipation contributions in TDDM as well as their interrelations. We also discuss grid artifacts and energy budget errors using these to compare the different models. Our results confirm the hypothesis that residual-stress dissipation reduces the necessary artificial dissipation. Because of the numerical ill-conditioning of deconvolution, whether temporal or spatial, there are practical limitations in the size of the filter width. Due to these limitations, the impact remains relatively minor. The a posteriori results of the new spatial regularization term show it to be effective in eliminating energy from the high wavenumber range. [ABSTRACT FROM AUTHOR]

In this work, the energy transfer in gas-surface collisions is investigated using the molecular dynamics method. The numerical setup consists of a nitrogen molecule scattering from a graphite surface. The main focus is put on the energy redistribution between different molecular kinetic modes and the surface for the case of strong thermal non-equilibrium. The thermal non-equilibrium is defined as the state when either translational or rotational temperature of impinging molecules differs significantly from that of the surface. Accordingly, two different scenarios have been examined, including rotational and translational excitation of the initial molecular state. In contrast to the molecular beam method, the initial molecular velocities are sampled from the equilibrium Maxwellian distribution, ensuring isotropic incidence angles and energies. The obtained results are expressed in the form of energy transfer coefficients, which are used to quantify the normalized energy loss or gain in a specific mode. Furthermore, the velocity distributions of reflected molecules are analyzed and compared with some of the available wall kernels, providing further insight into the nature of the energy transfer dynamics and scattering process. Additionally, the numerical setup is tested against the available molecular beam experimental data and the obtained results were used to select a suitable numerical force field. [ABSTRACT FROM AUTHOR]

Recently, a parallel Fokker–Planck-DSMC algorithm for rarefied gas flow simulation in complex domains at all Knudsen numbers was developed by the authors. Fokker–Planck-DSMC (FP-DSMC) is an augmentation of the classical DSMC algorithm, which mitigates the near-continuum deficiencies in terms of computational cost of pure DSMC. At each time step, based on a local Knudsen number criterion, the discrete DSMC collision operator is dynamically switched to the Fokker–Planck operator, which is based on the integration of continuous stochastic processes in time, and has fixed computational cost per particle, rather than per collision. In this contribution, we present an extension of the previous implementation with automatic local mesh refinement and parallel load-balancing. In particular, we show how the properties of discrete approximations to space-filling curves enable an efficient implementation. Exemplary numerical studies highlight the capabilities of the new code. [ABSTRACT FROM AUTHOR]

The process of cleaning microfiltration membranes contaminated with soybean oil, using pure supercritical carbon dioxide as cleaning fluid, was considered. A mathematical model of the process was developed, implemented into CFD software and validated using experimental results. The mathematical model is based on the Volume of Fluid approach and includes porous zone treatment, variable fluid phase composition due to mutual solubility of the contaminant and the solvent, as well as phase transition. The developed model was implemented into the OpenFOAM toolbox and validated using experimental results. The results of CFD simulations using the mathematical model show a good agreement with experimental results. CFD simulations were performed in order to analyze the effect of solvent flow rate and the effect of oil phase swelling on the course of the process. The mass transfer mechanisms were identified. The developed model is an efficient tool for process optimization, scale-up, and high-pressure equipment design. [ABSTRACT FROM AUTHOR]

In this paper, a numerical model to predict flow-induced shear failure along pre-existing fractures is presented. The framework is based on a discrete fracture representation embedded in a continuum describing the damaged matrix. A finite volume method is used to compute both flow and mechanical equilibrium, whereas specifically tailored basis functions are used to account for the physics at discontinuities. The failure criterion is based on a maximum shear strength limit, which changes with varying compressive stress on the fracture manifold. The displacements along fracture manifolds are obtained such that force balance is achieved under conditions, where shear stress of the failing fracture segment is constrained to the maximum shear strength at the segment. Simultaneously, the fluid pressure is computed independently of the shear slip. A relaxation model approach is used to obtain the maximum shear limit on the fracture manifold, which leads to grid convergence. [ABSTRACT FROM AUTHOR]

In the context of flow and transport in porous and fractured media, Darcy-based continuum models, while computationally inexpensive, are of limited use when the scale of interest is of similar size or smaller than the characteristic network connection length. Recently, we have outlined a non-local Darcy model that bridges the gap between network and Darcy-based descriptions. This formulation is able to account for non-local pressure effects that are not accounted for in a classical Darcy description. At the heart of this non-local flow formulation is a conductivity distribution or kernel that is related to the scalar permeability in the classical Darcy law. In this paper, ensembles of flow networks are considered, of which the necessary statistical information is assumed to be known. In order to relate the conductivity distribution with the flow statistics, a stochastic transport model for fluid particles, termed generalized continuous time random walk (g-CTRW), which is a generalization of correlated continuous time random walk, is introduced. Note that similar assumptions as for correlated CTRW are made, i.e., that lengths and velocities of connections between successive nodes along the trajectories can be described by Markov processes. In order to proceed with a theoretical analysis, a Boltzmann equation is presented, which is consistent with the particle time marching algorithm based on g-CTRW. An important outcome of the analysis is an expression relating the joint probability density function of velocity and connection length in the networks with the conductivity kernel. A numerical, stationary flow example demonstrates how the kernel can be extracted. Further, an algorithm is proposed to compute consistent velocity statistics, mean pressure distribution, and spatially varying conductivity kernel in the case of non-stationary flow. This coupled iterative approach is an attempt to consistently compute stochastic flow and transport in large network ensembles. [ABSTRACT FROM AUTHOR]

A recently introduced subphase framework for modeling the nonwetting phase relative permeability is extended to the wetting phase. Within this framework, the wetting phase is divided into four subphases, which are distinguished by their connectivity; backbone, dendritic, isolated and corner-film subphases. The subphase saturations evolve according to inter-subphase volume transfer terms, which require modeling. An advantage of distinguishing the subphases is that wetting phase relative permeability relations as functions of these constituent subphases can be developed. In order to develop models for the inter-subphase volume transfer and the wetting phase relative permeability in a strongly wetted system, quasi-static flow simulations in pore networks were conducted to analyze the evolution of the wetting subphases during drainage and imbibition. The simulation results suggest that hysteresis trends apparent in experimentally obtained wetting phase relative permeability curves for Berea sandstone may be explained by accounting for corner-film flow. [ABSTRACT FROM AUTHOR]

A finite volume-based numerical modeling framework using a hierarchical fracture representation (HFR) has been developed to compute flow-induced shear failure. To accurately capture the mechanics near fracture manifolds, discontinuous basis functions are employed which ensure continuity of the displacement gradient across fractures. With these special basis functions, traction and compressive forces on the fracture segment can be calculated without any additional constraints, which is extremely useful for estimating the irreversible displacement along the fracture (slip) based on a constitutive friction law. The method is further extended to include slip-dependent hydraulic aperture change and grid convergent results are obtained. Further, the change in hydraulic aperture is modeled using an asymptotic representation which respects the experimentally observed behavior of pore volume dilation due to shear slip. The model allows the initial rapid increase in hydraulic aperture due to shear slip and asymptotically approaches a finite value after repeated shearing of a fracture segment. This aperture increase is the only feedback for mechanics into the fluid flow for a linear elastic mechanics problem. The same model is also extended to include poroelastic relations between flow and mechanics solver. The grid convergence result in the case of poroelastic flow-mechanics coupling for flow-induced shear failure is also obtained. This proves the robustness of the numerical and analytical modeling of fracture and friction in the extended finite volume method (XFVM) set-up. Finally, a grid convergent result for seismic moment magnitude for single fracture and fracture network with random initial hydraulic and friction properties is also obtained. The b-value, which represents the slope of seismic moment occurrence frequency decay vs seismic moment magnitude, which is approximately constant in a semi-logarithmic plot, is estimated. The numerical method leads to converged b-values for both single fracture and fracture network simulations, as grid and time resolutions are increased. For the resulting linear system, a sequential approach is used, that is, first, the flow and then the mechanics problems are solved. The new modeling framework is very useful to predict seismicity, permeability, and flow evolution in geological reservoirs. This is demonstrated with numerical simulations of enhancing a geothermal system. [ABSTRACT FROM AUTHOR]

Pore-network models of porous media are useful in the study of pore-scale flow in porous media. In order to extract macroscopic properties from flow simulations in pore-networks, it is crucial the networks are large enough to be considered representative elementary volumes. However, existing two-phase network flow solvers are limited to relatively small domains. For this purpose, a multi-scale pore-network (MSPN) method, which takes into account flow-rate effects and can simulate larger domains compared to existing methods, was developed. In our solution algorithm, a large pore network is partitioned into several smaller sub-networks. The algorithm to advance the fluid interfaces within each subnetwork consists of three steps. First, a global pressure problem on the network is solved approximately using the multiscale finite volume (MSFV) method. Next, the fluxes across the subnetworks are computed. Lastly, using fluxes as boundary conditions, a dynamic two-phase flow solver is used to advance the solution in time. Simulation results of drainage scenarios at different capillary numbers and unfavourable viscosity ratios are presented and used to validate the MSPN method against solutions obtained by an existing dynamic network flow solver. [ABSTRACT FROM AUTHOR]

Turbulent reactive flows laden with droplets appear in various energy systems but are difficult to understand and parametrize. Such flows involve interactions of turbulent fluctuations, phase changes, and chemical reactions that give rise to complex phenomena. To improve our knowledge, we performed direct numerical simulations of a canonical shear flow. It is composed of a hot, quiescent outer layer and a cold, turbulent inner layer that is laden with droplets. Due to the turbulent fluctuations, the droplets form clusters. Due to the high temperatures, the droplets evaporate quickly and flames emerge spontaneously at the interface of the two layers. We observed premixed flames that enclose droplet clusters and diffusion flames that enclose vapor pockets or single droplets. To examine these flame structures in more detail, we varied the droplet size, droplet loading, and shear rate. We found that the droplet size and droplet loading have significant effects, whereas the shear rate has only subtle effects. [ABSTRACT FROM AUTHOR]

In this work, the zonal Multiscale Finite Volume (zMSFV) framework is presented. The framework generalizes previous extensions of the Multiscale Finite Volume (MSFV) method and allows to integrate additional models in a unified way. The new approach is based on splitting the domain of interest into a classical MSFV domain and additional zones. Within each zone, the solution space is spanned by so-called zonal functions. Coupling of the zonal solutions to the surrounding domain is achieved via extended zonal functions. The construction of basis, zonal and extended zonal functions can be performed such that the functions form a partition of unity. The zMSFV framework allows to include the influence of the zonal functions directly in the coarse-scale problem. Similar to previous MSFV method formulations, the zMSFV framework can ensure conservative coarse-scale solutions and allows for the construction of conservative fine-scale solutions. The main features of the zMSFV framework are used to derive robust preconditioners for iterative solutions of high-contrast problems as encountered in subsurface flow and transport simulations. It is shown that the obtained convergence rates are independent of the contrast. [ABSTRACT FROM AUTHOR]

A major challenge for the conventional Direct Simulation Monte Carlo ( DSMC ) technique lies in the fact that its computational cost becomes prohibitive in the near continuum regime, where the Knudsen number ( Kn )—characterizing the degree of rarefaction—becomes small. In contrast, the Fokker–Planck ( FP ) based particle Monte Carlo scheme allows for computationally efficient simulations of rarefied gas flows in the low and intermediate Kn regime. The Fokker–Planck collision operator—instead of performing binary collisions employed by the DSMC method—integrates continuous stochastic processes for the phase space evolution in time. This allows for time step and grid cell sizes larger than the respective collisional scales required by DSMC . Dynamically switching between the FP and the DSMC collision operators in each computational cell is the basis of the combined FP-DSMC method, which has been proven successful in simulating flows covering the whole Kn range. Until recently, this algorithm had only been applied to two-dimensional test cases. In this contribution, we present the first general purpose implementation of the combined FP-DSMC method. Utilizing both shared- and distributed-memory parallelization, this implementation provides the capability for simulations involving many particles and complex geometries by exploiting state of the art computer cluster technologies. [ABSTRACT FROM AUTHOR]

The underlying premise of temporal large eddy simulation (TLES) is that the attenuation of high-frequency content also attenuates the high-wavenumber content. Yet, to date, the effect in wavenumber space of removing high-frequency oscillations by time-domain filtering is not well understood. In this work, we numerically investigate the relationship between the frequency and wavenumber with particular attention to the role of the temporal residual-stress in TLES. Moreover, since under-resolved simulations that use high-order, non-dissipative numerical methods require some measure of artificial dissipation for stabilization, we also discuss the regularization term with practical relevance to under-resolved applications of TLES. Specifically, we analyze the effects of Eulerian time-domain filtering with a causal exponential filter on homogeneous isotropic turbulence. The data are generated by direct numerical simulation of the Navier–Stokes equations, which are driven to maintain an average Reynolds number (R e λ ) of 200. A priori, Fourier transformations of the velocity fields were performed in order to compute the unfiltered and filtered energy and dissipation spectra in both wavenumber space and wavenumber–frequency space. Furthermore, the amount of unresolved dissipation of an insufficiently resolved simulation was approximated in an attempt to estimate the required additional artificial dissipation. The results indicate that the numerically motivated stabilization term can be reduced due to temporal filtering. Moreover, it has been shown that a sharp cutoff in the frequency domain does not translate into a sharp cutoff in the wavenumber space. Thus, a hybrid model that combines temporal filtering for the residual-stress and spatial filtering for stabilization might be advantageous. [ABSTRACT FROM AUTHOR]

A Fokker–Planck based particle Monte Carlo algorithm was devised recently for simulations of rarefied gas flows by the authors [1–3] . The main motivation behind the Fokker–Planck (FP) model is computational efficiency, which could be gained due to the fact that the resulting stochastic processes are continuous in velocity space. This property of the model leads to simulations where the computational cost becomes independent of the Knudsen number (Kn) [3] . However, the Fokker–Planck model which can be seen as a diffusion approximation of the Boltzmann equation, becomes less accurate as Kn increases. In this study we propose a hybrid Fokker–Planck–Direct Simulation Monte Carlo (FP–DSMC) solution method, which is applicable for the whole range of Kn. The objective of this algorithm is to retain the efficiency of the FP scheme at low Kn ( Kn ≪ 1 ) and to employ conventional DSMC at high Kn ( Kn ≫ 1 ). Since the computational particles employed by the FP model represent the same data as in DSMC, the coupling between the two methods is straightforward. The new ingredient is a switching criterion which would ideally result in a hybrid scheme with the efficiency of the FP method and the accuracy of DSMC for the whole Kn-range. Here, we adopt the number of collisions in a given computational cell and for a given time step size as a decision criterion in order to switch between the FP model and DSMC. For assessment of the hybrid algorithm, different test cases including flow impingement and flow expansion through a slit were studied. Both accuracy and efficiency of the model are shown to be excellent for the presented test cases. [ABSTRACT FROM AUTHOR]

This work presents a kinetic wall boundary model for diatomic gas molecules. The model is derived by generalizing the Cercignani-Lampis-Lord gas-surface interaction kernel in order to account for the gas internal degrees of freedom. Here, opposed to the extensions by Lord ["Some extensions to the Cercignani-Lampis gas-surface scattering kernel," Phys. Fluids 3, 706-710 (1991)], energy exchange between different molecular modes is honored and thus, different physical phenomena arising from inelastic gas-surface collisions can be described. For practical implementations of the model, a Monte-Carlo algorithm was devised, which significantly reduces the computational cost associated with sampling. Comparisons of model predictions with experimental and molecular dynamics data exhibit good agreement. Moreover, simulation studies are performed to demonstrate how energy transfers between different modes due to wall collisions can be exploited for gas separation. [ABSTRACT FROM AUTHOR]

The multiscale finite volume (MSFV) method was designed to efficiently compute approximate numerical solutions of elliptic and parabolic problems with highly heterogeneous coefficients. For a wide range of test cases, it has been demonstrated that MSFV solutions are in excellent agreement with reference data obtained with a standard fine-scale finite-volume method. However, for some problems involving large coherent structures with strong contrasts (e.g., channels and shale layers), the MSFV method produces unsatisfactory results due to the dwindling validity of the localization assumption. Recently, the iterative MSFV (i-MSFV) method was introduced to iteratively improve the localization assumption, and it was shown that the method converges to the fine-scale reference solution. In this work, it is explained how the convergence rate of the i-MSFV method can be enhanced by consistent enrichment of the initial coarse space spanned by nodal basis functions. A new set of enrichment basis functions associated with additional coarse-scale degrees of freedom (DoF) is introduced. By construction, the sum of all nodal and enrichment basis functions is one in the entire computational domain. Further, a hybrid finite-volume/Galerkin formulation for the coarse-scale problem and a generic placement strategy for the additional DoF are devised. The resulting iterative Galerkin-enriched MSFV (i-Ge-MSFV) method has all features of the i-MSFV method, but is more robust and has improved convergence properties. [ABSTRACT FROM AUTHOR]

An adaptive conservative time integration scheme (ACTI) for compressible flow simulations is devised. A finite volume method is used, in which every cell employs a time step size which is some power of two times smaller than a global time step. By first advancing those cells with smaller time steps, this allows to use the already computed accumulated fluxes when the adjacent cells with larger time steps catch up. Conservation and periodic synchronization are thus guaranteed by construction; both important advantages of the new scheme (especially in the presence of shock waves) compared to previously proposed adaptive time stepping methods for compressible flow. Accuracy and computational speedup are demonstrated for challenging 1D and 2D test cases. Comparisons of ACTI results with an analytical solution and with results obtained without ACTI show excellent agreement. Although maximum wave speeds and/or cell sizes vary by several orders of magnitude throughout the computational domains, the CFL numbers employed by ACTI in each cell vary not more than by approximately a factor of two. Without ACTI, on the other hand, the CFL numbers are tiny in most of the cells. Since this results in a dramatic reduction of required flux computations, high speedup gains are achieved due to ACTI; in particular, if only few cells experience a very small time step, while the time step size limitations are less severe for the majority of cells. • Explicit adaptive time integration for compressible flow. • Strictly conservative - is of great importance especially in the presence of shocks. • Piecewise linear reconstruction in space and time - is important for accuracy. • Total number of flux computations and cell value updates can be drastically reduced. • Proposed scheme is robust and can be integrated immediately into existing codes. [ABSTRACT FROM AUTHOR]

Abstract: This paper is devoted to the algorithmic improvement and careful analysis of the Fokker–Planck kinetic model derived by Jenny et al. [1] and Gorji et al. [2]. The motivation behind the Fokker–Planck based particle methods is to gain efficiency in low Knudsen rarefied gas flow simulations, where conventional direct simulation Monte Carlo (DSMC) becomes expensive. This can be achieved due to the fact that the resulting model equations are continuous stochastic differential equations in velocity space. Accordingly, the computational particles evolve along independent stochastic paths and thus no collision needs to be calculated. Therefore the computational cost of the solution algorithm becomes independent of the Knudsen number. In the present study, different computational improvements were persuaded in order to augment the method, including an accurate time integration scheme, local time stepping and noise reduction. For assessment of the performance, gas flow around a cylinder and lid driven cavity flow were studied. Convergence rates, accuracy and computational costs were compared with respect to DSMC for a range of Knudsen numbers (from hydrodynamic regime up to above one). In all the considered cases, the model together with the proposed scheme give rise to very efficient yet accurate solution algorithms. [Copyright &y& Elsevier]

Abstract: Monte Carlo (MC) is a well known method for quantifying uncertainty arising for example in subsurface flow problems. Although robust and easy to implement, MC suffers from slow convergence. Extending MC by means of multigrid techniques yields the multilevel Monte Carlo (MLMC) method. MLMC has proven to greatly accelerate MC for several applications including stochastic ordinary differential equations in finance, elliptic stochastic partial differential equations and also hyperbolic problems. In this study, MLMC is combined with a streamline-based solver to assess uncertain two phase flow and Buckley–Leverett transport in random heterogeneous porous media. The performance of MLMC is compared to MC for a two dimensional reservoir with a multi-point Gaussian logarithmic permeability field. The influence of the variance and the correlation length of the logarithmic permeability on the MLMC performance is studied. [Copyright &y& Elsevier]

Abstract: Different simulation methods are applicable to study turbulent mixing. When applying probability density function (PDF) methods, turbulent transport, and chemical reactions appear in closed form, which is not the case in second moment closure methods (RANS). Moreover, PDF methods provide the entire joint velocity-scalar PDF instead of a limited set of moments. In PDF methods, however, a mixing model is required to account for molecular diffusion. In joint velocity-scalar PDF methods, mixing models should also account for the joint velocity-scalar statistics, which is often under appreciated in applications. The interaction by exchange with the conditional mean (IECM) model accounts for these joint statistics, but requires velocity-conditional scalar means that are expensive to compute in spatially three dimensional settings. In this work, two alternative mixing models are presented that provide more accurate PDF predictions at reduced computational cost compared to the IECM model, since no conditional moments have to be computed. All models are tested for different mixing benchmark cases and their computational efficiencies are inspected thoroughly. The benchmark cases involve statistically homogeneous and inhomogeneous settings dealing with three streams that are characterized by two passive scalars. The inhomogeneous case clearly illustrates the importance of accounting for joint velocity-scalar statistics in the mixing model. Failure to do so leads to significant errors in the resulting scalar means, variances and other statistics. [Copyright &y& Elsevier]

A Fokker-Planck based kinetic model is presented here, which also accounts for internal energy modes characteristic for diatomic gas molecules. The model is based on a Fokker-Planck approximation of the Boltzmann equation for monatomic molecules, whereas phenomenological principles were employed for the derivation. It is shown that the model honors the equipartition theorem in equilibrium and fulfills the Landau-Teller relaxation equations for internal degrees of freedom. The objective behind this approximate kinetic model is accuracy at reasonably low computational cost. This can be achieved due to the fact that the resulting stochastic differential equations are continuous in time; therefore, no collisions between the simulated particles have to be calculated. Besides, because of the devised energy conserving time integration scheme, it is not required to resolve the collisional scales, i.e., the mean collision time and the mean free path of molecules. This, of course, gives rise to much more efficient simulations with respect to other particle methods, especially the conventional direct simulation Monte Carlo (DSMC), for small and moderate Knudsen numbers. To examine the new approach, first the computational cost of the model was compared with respect to DSMC, where significant speed up could be obtained for small Knudsen numbers. Second, the structure of a high Mach shock (in nitrogen) was studied, and the good performance of the model for such out of equilibrium conditions could be demonstrated. At last, a hypersonic flow of nitrogen over a wedge was studied, where good agreement with respect to DSMC (with level to level transition model) for vibrational and translational temperatures is shown. [ABSTRACT FROM AUTHOR]

Abstract: In a real turbulent spray flame, dispersion, continuous phase turbulence modification, dispersed phase inter-particle collisions, evaporation, mixing and combustion occur simultaneously. Dealing with all these complexities and their interactions poses a tremendous modeling task. Therefore, in order to advance current modeling capabilities, it seems reasonable to aim for progress in individual sub-areas like breakup, dispersion, mixing and combustion, which however cannot be viewed in complete isolation. Further, one has to consider advantages and disadvantages of the general modeling approaches, which are direct numerical simulation (DNS), large eddy simulation (LES), simulations based on Reynolds averaged equations and probability density function (PDF) methods. Not least one also has to distinguish between Eulerian and Lagrangian dispersed phase descriptions. The goal of this paper is to provide a review of computational model developments relevant for turbulent dilute spray combustion, i.e. the dense regime, including collisions as well as primary and secondary atomization, is not covered. Also not considered is breakup in dilute sprays, which can occur in the presence of sufficiently high local turbulence. It is intended to guide readers interested in theory, in the development and validation of predictive models, and in planning new experiments. In terms of physical phenomena, the current understanding regarding turbulence modification due to droplets, preferential droplet concentration, impact on evaporation and micro-mixing, and different spray combustion regimes is summarized. In terms of modeling, different sets of equations are discussed, i.e. the governing conservation laws without and with point droplet approximation as employed by DNS, the filtered equations considered in LES, the Reynolds averaged equations, and Lagrangian evolution equations. Further, small scale models required in the context of point droplet approximations are covered. In terms of computational studies and method developments, progress is categorized by the employed approaches, i.e. DNS, LES, simulations based on Reynolds averaged equations, and PDF methods. In terms of experiments, various canonical spray flame configurations are discussed. Moreover, some of the most important experiments in this field are presented in a structured way with the intention to provide a database for model validation and a guideline for future investigations. [Copyright &y& Elsevier]

Abstract: In this work, we propose a consistent turbulence-modeling framework for hybrid LES/RANS modeling. In this framework, the filtered and Reynolds averaged Navier–Stokes (RANS) equations are solved simultaneously in the whole domain on their respective meshes. Consistency between the two solutions is achieved in terms of velocity, pressure, and turbulent quantities through additional drift terms in the corresponding equations. This approach leads to clean conditions at the LES/RANS interfaces. Note that this general framework does not depend on the specific choice of LES and RANS models. A hybrid LES/RANS solver is developed within this framework and used to simulate the flow in a plane channel and that in a channel with periodic hills. The results demonstrate that the hybrid solver leads to significantly improved results with moderate computational overhead compared to traditional LES, making it a promising candidate for industrial flow simulations. [Copyright &y& Elsevier]

Abstract: The Karhunen–Loeve (KL) decomposition and the polynomial chaos (PC) expansion are elegant and efficient tools for uncertainty propagation in porous media. Over recent years, KL/PC-based frameworks have successfully been applied in several contributions for the flow problem in the subsurface context. It was also shown, however, that the accurate solution of the transport problem with KL/PC techniques is more challenging. We propose a framework that utilizes KL/PC in combination with sparse Smolyak quadrature for the flow problem only. In a subsequent step, a Lagrangian sampling technique is used for transport. The flow field samples are calculated based on a PC expansion derived from the solutions at relatively few quadrature points. To increase the computational efficiency of the PC-based flow field sampling, a new reduction method is applied. For advection dominated transport scenarios, where a Lagrangian approach is applicable, the proposed PC/Monte Carlo method (PCMCM) is very efficient and avoids accuracy problems that arise when applying KL/PC techniques to both flow and transport. The applicability of PCMCM is demonstrated for transport simulations in multivariate Gaussian log-conductivity fields that are unconditional and conditional on conductivity measurements. [Copyright &y& Elsevier]

Abstract: The multiscale finite volume (MSFV) method is a computationally efficient numerical method for the solution of elliptic and parabolic problems with heterogeneous coefficients. It has been shown for a wide range of test cases that the MSFV results are in close agreement with those obtained with a classical (computationally expensive) technique. The method, however, fails to give accurate results for highly anisotropic heterogeneous problems due to weak localization assumptions. Recently, a convergent iterative MSFV (i-MSFV) method was developed to enhance the quality of the multiscale results by improving the localization conditions. Although the i-MSFV method proved to be efficient for most practical problems, it is still favorable to improve the localization condition adaptively, i.e. only for a sub-domain where the original MSFV localization conditions are not acceptable, e.g. near shale layers and long coherent structures with high permeability contrasts. In this paper, a space–time adaptive i-MSFV (ai-MSFV) method is introduced. It is shown how to improve the MSFV results adaptively in space and simulation time. The fine-scale smoother, which is necessary for convergence of the i-MSFV method, is also applied locally. Finally, for multiphase flow problems, two criteria are investigated for adaptively updating the MSFV interpolation functions: (1) a criterion based on the total mobility change for the transient coefficients and (2) a criterion based on the pressure equation residual for the accuracy of the results. For various challenging test cases it is demonstrated that iterations in order to obtain accurate results even for highly anisotropic heterogeneous problems are required only in small sub-domains and not everywhere. The findings show that the error introduced in the MSFV framework can be controlled and improved very efficiently with very little additional computational cost compared to the original, non-iterative MSFV method. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a stochastic model is presented to simulate the flow of gases, which are not in thermodynamic equilibrium, like in rarefied or micro situations. For the interaction of a particle with others, statistical moments of the local ensemble have to be evaluated, but unlike in molecular dynamics simulations or DSMC, no collisions between computational particles are considered. In addition, a novel integration technique allows for time steps independent of the stochastic time scale. The stochastic model represents a Fokker–Planck equation in the kinetic description, which can be viewed as an approximation to the Boltzmann equation. This allows for a rigorous investigation of the relation between the new model and classical fluid and kinetic equations. The fluid dynamic equations of Navier–Stokes and Fourier are fully recovered for small relaxation times, while for larger values the new model extents into the kinetic regime. Numerical studies demonstrate that the stochastic model is consistent with Navier–Stokes in that limit, but also that the results become significantly different, if the conditions for equilibrium are invalid. The application to the Knudsen paradox demonstrates the correctness and relevance of this development, and comparisons with existing kinetic equations and standard solution algorithms reveal its advantages. Moreover, results of a test case with geometrically complex boundaries are presented. [Copyright &y& Elsevier]

Abstract: This paper addresses the convergence properties of implicit numerical solution algorithms for nonlinear hyperbolic transport problems. It is shown that the Newton–Raphson (NR) method converges for any time step size, if the flux function is convex, concave, or linear, which is, in general, the case for CFD problems. In some problems, e.g., multiphase flow in porous media, the nonlinear flux function is S-shaped (not uniformly convex or concave); as a result, a standard NR iteration can diverge for large time steps, even if an implicit discretization scheme is used to solve the nonlinear system of equations. In practice, when such convergence difficulties are encountered, the current time step is cut, previous iterations are discarded, a smaller time step size is tried, and the NR process is repeated. The criteria for time step cutting and selection are usually based on heuristics that limit the allowable change in the solution over a time step and/or NR iteration. Here, we propose a simple modification to the NR iteration scheme for conservation laws with S-shaped flux functions that converges for any time step size. The new scheme allows one to choose the time step size based on accuracy consideration only without worrying about the convergence behavior of the nonlinear solver. The proposed method can be implemented in an existing simulator, e.g., for CO2 sequestration or reservoir flow modeling, quite easily. The numerical analysis is confirmed with simulation studies using various test cases of nonlinear multiphase transport in porous media. The analysis and numerical experiments demonstrate that the modified scheme allows for the use of arbitrarily large time steps for this class of problems. [Copyright &y& Elsevier]

In the present study, a unified probability density function formulation for capturing the phenomena of turbulence modification of the continuous phase due to the dispersed phase turbulence is presented. A stochastic model based on dispersed phase turbulence length scale has been proposed for the purpose. The model has been validated with experimental data [Poelma et al., “Particle fluid interactions in grid-generated turbulence,” J. Fluid Mech. 589, 315 (2007)] on the decay of turbulence of the flow seeded with ceramic particles in a vertical recirculating water channel. The obtained simulation results are in good agreement with the experimental data. Numerical experiments have been performed to investigate the influence of gravity on the decay of the continuous phase Reynolds stresses. For comparison, the influence of dispersed phase turbulence on the continuous phase turbulence without taking gravity into consideration has also been studied. [ABSTRACT FROM AUTHOR]

Abstract: The multiscale finite-volume (MSFV) method was originally developed for the solution of heterogeneous elliptic problems with reduced computational cost. Recently, some extensions of this method for parabolic problems have been proposed. These extensions proved effective for many cases, however, they are neither general nor completely satisfactory. For instance, they are not suitable for correctly capturing the transient behavior described by the parabolic pressure equation. In this paper, we present a general multiscale finite-volume method for parabolic problems arising, for example, from compressible multiphase flow in porous media. Opposed to previous methods, here, the basis and correction functions are solutions of full parabolic governing equations in localized domains. At the same time, to enhance the computational efficiency of the scheme, the basis functions are kept pressure independent and do not have to be recalculated as pressure evolves. This general approach requires no additional assumptions and its good efficiency and high accuracy is demonstrated for various challenging test cases. Finally, to improve the quality of the results and also to extend the scheme for highly anisotropic heterogeneous problems, it is combined with the iterative MSFV (i-MSFV) method for parabolic problems. As one iterates, the i-MSFV solutions of compressible multiphase problems (parabolic problems) converge to the corresponding fine-scale reference solutions in the same way as demonstrated recently for incompressible cases (elliptic problems). Therefore, the proposed MSFV method can also be regarded as an efficient linear solver for parabolic problems and studies of its efficiency are presented for many test cases. [Copyright &y& Elsevier]

Abstract: The iterative-multi-scale-finite-volume (IMSFV) procedure is applied as an efficient solver for the pressure Poisson equation arising in numerical methods for the simulation of incompressible flows with the immersed-interface method (IIM). Motivated by the requirements of the specific IIM implementation, a modified version of the IMSFV algorithm is presented to allow the solution of problems, in which the varying coefficient of the elliptic equation (e.g. the permeability of the medium in the context of the simulation of flows in porous media) varies over several orders of magnitude or even becomes zero within the integration domain. Furthermore, a strategy is proposed to incorporate the iterative procedure needed by the IIM to converge out constraints at immersed boundaries into the iterative IMSFV cycle. No significant deterioration of performance of the IMSFV method is observed with respect to cases, in which no iterative improvement of the boundary conditions is considered. [Copyright &y& Elsevier]

Abstract: In the present study, a framework for modeling two-phase evaporating flow is presented, which employs an Eulerian–Lagrangian–Lagrangian approach. For the continuous phase, a joint velocity-composition probability density function (PDF) method is used. Opposed to other approaches, such PDF methods require no modeling for turbulent convection and chemical source terms. For the dispersed phase, the PDF of velocity, diameter, temperature, seen gas velocity and seen gas composition is calculated. This provides a unified formulation, which allows to consistently address the different modeling issues associated with such a system. Because of the high dimensionality, particle methods are employed to solve the PDF transport equations. To further enhance computational efficiency, a local particle time-stepping algorithm is implemented and a particle time-averaging technique is employed to reduce statistical and bias errors. In comparison to previous studies, a significantly smaller number of droplet particles per grid cell can be employed for the computations, which rely on two-way coupling between the droplet and gas phases. The framework was validated using established experimental data and a good overall agreement can be observed. [Copyright &y& Elsevier]

Abstract: In transported probability density function and filtered density function methods, micromixing models are required to close the molecular mixing term. The accuracy and computational efficiency of improved versions of the parameterized scalar profile (PSP) model are assessed and compared with commonly used mixing models such as Curl, modified Curl, interaction by exchange with the mean and Euclidean minimum spanning tree. Different generalizations of the PSP mixing model for spatially inhomogeneous flow configurations are presented. The selected test cases focus on molecular mixing and avoid interference with other models. Simulation results for a three-stream problem, involving two inert scalars, and a multi-scalar test case with mean-scalar-gradients are presented. [Copyright &y& Elsevier]

Abstract: In this paper, an extension of the multi-scale finite-volume (MSFV) method is devised, which allows to simulate flow and transport in reservoirs with complex well configurations. The new framework fits nicely into the data structure of the original MSFV method and has the important property that large patches covering the whole well are not required. For each well, an additional degree of freedom is introduced. While the treatment of pressure-constraint wells is trivial (the well-bore reference pressure is explicitly specified), additional equations have to be solved to obtain the unknown well-bore pressure of rate-constraint wells. Numerical simulations of test cases with multiple complex wells demonstrate the ability of the new algorithm to capture the interference between the various wells and the reservoir accurately. [Copyright &y& Elsevier]

Abstract: For the calculation of nonpremixed turbulent flames with thin reaction zones the joint probability density function (PDF) of the mixture fraction and its dissipation rate plays an important role. The corresponding PDF transport equation involves a mixing model for the closure of the molecular mixing term. Here, the parameterized scalar profile (PSP) mixing model is extended to provide the required joint statistics. Model predictions are validated using direct numerical simulation (DNS) data of a passive scalar mixing in a statistically homogeneous turbulent flow. Comparisons between the DNS and the model predictions are provided, which involve different initial scalar-field lengthscales. [Copyright &y& Elsevier]

Abstract: Many of the complex physical processes relevant for compositional multi-phase flow in porous media are well understood at the pore-scale level. In order to study CO2 storage in sub-surface formations, however, it is not feasible to perform simulations at these small scales directly and effective models for multi-phase flow description at Darcy scale are needed. Unfortunately, in many cases it is not clear how the micro-scale knowledge can rigorously be translated into consistent macroscopic equations. Here, we present a new methodology, which provides a link between Lagrangian statistics of phase particle evolution and Darcy scale dynamics. Unlike in finite-volume methods, the evolution of Lagrangian particles representing small fluid phase volumes is modeled. Each particle has a state vector consisting of its position, velocity, fluid phase information and possibly other properties like phase composition. While the particles are transported through the computational domain according to their individual velocities, the properties are modeled via stochastic processes honoring specified Lagrangian statistics. Note that the conditional expectations of the particle velocities are different for different fluid phases. The goal of this paper is to present the general framework for this alternative modeling approach. Various one and two-dimensional numerical experiments demonstrate that with appropriate stochastic rules the particle solutions are consistent with a standard two-phase Darcy flow formulation. In the end, we demonstrate how to model non-equilibrium phenomena within the stochastic particle framework, which will be the main focus of the future work. [Copyright &y& Elsevier]

The multiscale finite-volume (MSFV) method has been designed to solve flow problems on large domains efficiently. First, a set of basis functions, which are local numerical solutions, is employed to construct a fine-scale pressure approximation; then a conservative fine-scale velocity approximation is constructed by solving local problems with boundary conditions obtained from the pressure approximation; finally, transport is solved at the fine scale. The method proved very robust and accurate for multiphase flow simulations in highly heterogeneous isotropic reservoirs with complex correlation structures. However, it has recently been pointed out that the fine-scale details of the MSFV solutions may be lost in the case of high anisotropy or large grid aspect ratios. This shortcoming is analyzed in this paper, and it is demonstrated that it is caused by the appearance of unphysical "circulation cells." We show that damped-shear boundary conditions for the conservative-velocity problems or linear boundary conditions for the basis-function problems can significantly improve the MSFV solution for highly anisotropic permeability fields without sensitively affecting the solution in the isotropic case. [ABSTRACT FROM AUTHOR]

Abstract: The Multiscale Finite-Volume (MSFV) method has been recently developed and tested for multiphase-flow problems with simplified physics (i.e. incompressible flow without gravity and capillary effects) and proved robust, accurate and efficient. However, applications to practical problems necessitate extensions that enable the method to deal with more complex processes. In this paper we present a modified version of the MSFV algorithm that provides a suitable and natural framework to include additional physics. The algorithm consists of four main steps: computation of the local basis functions, which are used to extract the coarse-scale effective transmissibilities; solution of the coarse-scale pressure equation; reconstruction of conservative fine-scale fluxes; and solution of the transport equations. Within this framework, we develop a MSFV method for compressible multiphase flow. The basic idea is to compute the basis functions as in the case of incompressible flow such that they remain independent of the pressure. The effects of compressibility are taken into account in the solution of the coarse-scale pressure equation and, if necessary, in the reconstruction of the fine-scale fluxes. We consider three models with an increasing level of complexity in the flux reconstruction and test them for highly compressible flows (tracer transport in gas flow, imbibition and drainage of partially saturated reservoirs, depletion of gas–water reservoirs, and flooding of oil–gas reservoirs). We demonstrate that the MSFV method provides accurate solutions for compressible multiphase flow problems. Whereas slightly compressible flows can be treated with a very simple model, a more sophisticate flux reconstruction is needed to obtain accurate fine-scale saturation fields in highly compressible flows. [Copyright &y& Elsevier]

Data assimilation (DA) plays a crucial role in extracting valuable information from flow measurements in fluid dynamics problems. Often only time-averaged data is available, which poses challenges for DA in the context of unsteady flow problems. Recent works have shown promising results in optimizing Reynolds-averaged Navier–Stokes (RANS) simulations of stationary flows using sparse data through variational data assimilation, enabling the reconstruction of mean flow profiles. In this study we perform three-dimensional variational data assimilation of sparse time-averaged data into an unsteady RANS (URANS) simulation by means of a stationary divergence-free forcing term in the URANS equations. Efficiency and speed of our method are enhanced by employing coarse URANS simulations and leveraging the stationary discrete adjoint method for the time-averaged URANS equations. The data assimilation codes were developed in-house using OpenFOAM for the URANS simulations as well as for the solution of the adjoint problem, and Python for the gradient-based optimization. Our results demonstrate that data assimilation of sparse time-averaged velocity measurements not only enables accurate mean flow reconstruction, but also improves the flow dynamics, specifically the vortex shedding frequency. To validate the efficacy of our approach, we applied it to turbulent flows around cylinders of various shapes at Reynolds numbers ranging from 3000 to 22000. Our findings indicate that data points near the cylinder play a crucial role in improving the vortex shedding frequency, while additional data points further downstream are necessary to also reconstruct the time-averaged velocity field in the wake region. [ABSTRACT FROM AUTHOR]

Fast fillings of hydrogen vehicles require proper control of the temperature to ensure the integrity of the storage tanks. This study presents an analysis of heat transfer during filling of a hydrogen tank. A conjugate heat transfer based on energy balance is introduced. The numerical model is validated against fast filling experiments of hydrogen in a Type IV tank by comparing the gas temperature evolution. The impact of filling parameters, such as initial temperature, inlet nozzle diameter and filling time is then assessed. For the considered Type IV tank, the results show that both a higher and lower tank shell thermal conductivity results in lower inner wall peak temperatures. The presented model provides an analytical description of the temperature evolution in the gas and in the tank shell, and is thus a useful tool to explore a broad range of parameters, e.g., to determine new hydrogen filling protocols. • An analytical model is developed to predict the tank shell temperature distribution. • The analytical model is validated against experimental results. • The influence of filling parameters on the tank wall peak temperature is assessed. • The tank materials heat diffusivity is the critical parameter for fast fillings. [ABSTRACT FROM AUTHOR]

• A particle-particle hybrid approach by combining the unified stochastic particle BGK (USPBGK) method and DSMC is developed. • The newly proposed hybrid method has second-order accuracy in the continuum regime due to the advantage of the USPBGK method. • Simplification of the original USPBGK method is introduced to conform with the computational framework of DSMC. • An equilibrium-breakdown criterion, which refers to the Knudsen number and is easy to be calculated in particle methods, is proposed. For the simulation of multiscale gas flows, the numerical scheme should be valid and efficient in both rarefied and continuum regimes. For example, the Direct Simulation Monte Carlo (DSMC) method is not appropriate because of its huge computational cost in the continuum regime. Various kinds of hybrid methods with DSMC have been proposed to deal with this difficulty. One of them is the particle-particle hybrid method, which combines DSMC with another stochastic particle method that is based on an approximate kinetic model, such as the BGK-DSMC hybrid method. Since the same kind of computational particles is applied in the stochastic particle BGK (SPBGK) and DSMC methods, they can be implemented in a unified particle framework. Therefore, compared to the CFD-DSMC hybrid method, the BGK-DSMC hybrid method avoids difficulties caused by the amalgamation of two fundamentally different types of solvers. However, the traditional SPBGK method decouples the molecular motions and collisions in analogy to DSMC, and hence its transport properties deviate from physical values as the time step size increases. This defect significantly affects its computational accuracy and efficiency in the continuum regime. In the present paper, instead of the traditional SPBGK method, a unified stochastic particle BGK (USPBGK) method, which has second-order accuracy in time and space, is combined with DSMC. Comparing the computational performance of the USPBGK-DSMC and BGK-DSMC hybrid methods for numerical test cases of hypersonic flows past a cylinder and plume flows out of a planar micronozzle, one note that the proposed USPBGK-DSMC hybrid method can achieve higher efficiency for such multiscale gas flow simulations. In addition, an equilibrium-breakdown criterion based on the ratio of the time scales of the macroscopic flow field and molecule collision is proposed as a switching criterion for the new hybrid method. This criterion depends on the local Knudsen number and is easy to implement in a unified particle framework. [ABSTRACT FROM AUTHOR]

In this paper the dynamics of human running on flat terrain and the required mechanical power output with its dependency on various parameters is investigated. Knowing the required mechanical power output is of relevance due to its relationship with the metabolic power. For example, a better understanding of the dependencies of required mechanical power output on weight, running and wind speed, step frequency, ground contact time etc. is very valuable for the assessment, analysis and optimization of running performance. Therefore, a mathematical model based on very few assumptions is devised. The purpose of the proposed model is to relate running speed and required mechanical power output as an algebraic function of the runner's mass, height, step rate, ground contact time and wind speed. This is relevant in order to better understand the mechanical energy cost of locomotion, and how much it depends on which parameters. The first of the main energy dissipation mechanisms is due to vertical oscillation, i.e., during each step some of the potential energy difference gets transformed into heat. The second mechanism is due to the anterior ground reaction force during the first part of stance and the third is due to aerodynamic drag. With the approximations of constant running speed and a sinusoidal vertical ground reaction force profile one obtains closed algebraic expressions for the center of mass trajectory and the required mechanical power output. Comparisons of model predictions and reported performance data suggest that approximately a quarter of the ground impact energy is stored during the first part of ground contact and then released during the remaining stance phase. Further, one can conclude from the model that less mechanical power output is required when running with higher step rates and a higher center of mass. Non intuitive is the result that a shorter ground contact time is beneficial for fast runs, while the opposite holds for slow runs. An important advantage of the devised model compared to others is that it leads to closed algebraic expressions for the center of mass trajectory and mechanical power output, which are functions of measurable quantities, i.e., of step rate, ground contact time, running speed, runner's mass, center of mass height, aerodynamic drag at some given speed, wind speed and heart rate. Moreover, the model relies on very few assumptions, which have been verified, and the only tuning parameter is the ratio of recovered elastic energy. [ABSTRACT FROM AUTHOR]

• An adaptive and still conservative time integration scheme for finite volume solvers. • In combination with a new flux solver the new sub-time stepping scheme is of almost second order (temporally and spatially). • The new adaptive conservative time integration scheme is robust and much faster (in some of the cases more than 50 times) than conventional time stepping (at almost the same accuracy). This is demonstrated in the paper with numerical studies. Finite volume methods for time dependent problems typically employ time integration schemes with constant time step sizes. The latter, in order to ensure stability and time accurate solutions, have to be chosen small enough, such that the Courant-Friedrichs-Lewy (CFL) number stays below a critical value everywhere. In many cases, however, this time step size limitation leads to huge numbers of very small time steps, which renders simulations very expensive. Motivated by this drawback of conventional time stepping schemes, various sub-time stepping algorithms have been proposed. However, most of them are inherently asynchronous, require small local CFL numbers or are not strictly conservative. In this paper a new adaptive time integration scheme for finite volume methods, which is conservative, of high spatial and temporal order, robust and easy to implement is presented. It relies on local sub-time steps which are fractions of a global time step by powers of two, i.e., the grid cells proceed asynchronously in the order of their termination time, but since they all synchronize at the end of each global time step, it is possible to guarantee continuity of the mean fluxes and thus strict conservation at the global time step resolution. Numerical experiments with 1D and 2D test cases demonstrate that the adaptive conservative time integration (ACTI) scheme can achieve extreme speed-up factors over conventional time integration, while still maintaining high spatial and temporal accuracy. [ABSTRACT FROM AUTHOR]