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The use of a contoured endwall has the potential to suppress endwall secondary flow. Unsteady wakes affect not only the boundary layer characteristics of blade suction surface at blade midspan but also the endwall flow structures. The lack of understanding of the flow mechanism of the combined effects of periodic wakes and contoured endwall on secondary flow limits their roles. This paper presents a experimental and numerical investigation of the endwall secondary flow in a typical high-lift low-pressure turbine cascade. Wakes were produced by moving rods upstream of cascade, and the flow fields at the exit of cascade were measured using a seven-hole pressure probe. The study focused on the combined effect of the upstream wakes and the contoured endwall on the secondary flow as well as the underlying physical mechanisms. The influences of the Reynolds numbers and the contoured endwall on the performance of high-lift low-pressure turbine endwall regions were also discussed. At steady conditions without wakes, the total losses in the turbine cascade increased with decreasing Reynolds number; the most intense passage vortex, counter vortex and corner vortex were observed at a low Reynolds number of 25,000 (based on the axial chord and the inlet velocity). The contoured endwall decreased the cross-passage pressure gradient, and suppressed the passage vortex. Under unsteady conditions, the interaction between upstream wakes and the passage vortex results in reduction of the passage vortex. The combined effect of the contoured endwall and periodic wakes redistributed the endwall pressure and further decreased the cross-passage pressure gradient. Consequently, the intensities of the passage vortex and counter vortex decreased by 17% and 11% respectively, compared with the flat endwall cascade with wakes. Contoured endwall with wakes reduced secondary kinetic energy of cascade exit by 53.8% than the result of the flat endwall no wake. Which is beneficial to improve the aerodynamic performance of the high-lift low-pressure turbine.

A new modeled Boltzmann equation (MBE) with four improvements made to conventional MBE is formulated. The first improvement is to include the particle internal rotational degree of freedom in the derivation of a continuous equilibrium velocity distribution function f eq; thus, rendering the MBE applicable to diatomic gas. The second improvement is made in the expansion assumed for fαeq in the lattice Boltzmann equation (LBE). This expansion is expressed in terms of the particle velocity vector (ξ) alone; hence, the LBE is no longer limited by a very low Mach number (M) assumption, and it also allows the LBE to correctly satisfy the zero divergence of the velocity field for incompressible flow. The third improvement is made to eliminate the bounce-back rule used to model no-slip wall boundary condition for fα because the rule leads to leakage at solid walls and mass conservation is compromised. The fourth improvement is carried out to render the modeled LBE truly valid for hydrodynamic flow simulation. Thus improved, the new lattice Boltzmann method (LBM) is no longer subject to the M

We deploy the immersogeometric approach for tracking moving objects. The method immerses objects into non-boundary-fitted meshes and weakly enforces Dirichlet boundary conditions on the object boundaries. The object motion is driven by the integrated surface force and external body forces. A residual-based variational multiscale method is employed to stabilize the finite element formulation for incompressible flows. Adaptively refined quadrature rules are used to better capture the geometry of the immersed boundaries by accurately integrating the intersected background elements. Treatment for the freshly-cleared nodes (i.e. background mesh nodes that are inside the object at one time step, but are in the fluid domain at the next time step) is considered. We assess the accuracy of the method by analyzing object motion in different flow structures including objects freely dropping in viscous fluids and particle focusing in unobstructed and obstructed micro-channels. We show that key quantities of interest are in very good agreements with analytical, numerical and experimental solutions. We also show a much better computational efficiency of this framework than current commercial codes using adaptive boundary-fitted approaches. We anticipate deploying this framework for applications of particle inertial migration in microfluidic channels.

This paper mainly investigates the combustion effects on the development of supersonic turbulent mixing layer flows. Firstly, the positivity-preserving limiter proposed by Hu et al. is extended to solve the unphysical negative species mass fraction problem of traditional WENO schemes for the first time. Then, the large eddy simulation (LES) of the supersonic turbulent mixing layer flow with convective Mach number being 0.61 under the inert and combustion conditions are conducted separately to investigate the combustion effects. The LES is conducted with the extending fifth-order positivity-preserving WENO scheme and great efforts are spent to reproduce the real flow situation by adopting the three dimensional space-developing method with detailed chemical reaction mechanism. The following conclusions are drawn. It is found that the combustion will obviously change the flow structures. The kinetic energy spectra are nearly not affected by the combustion effects but the temperature fluctuations are strengthened among all the resolved scales. The decreasing mechanism of mixing layer growth rate due to combustion heat release effects is found. The combustion heat release effects decrease the production of Reynolds stress. Then the Reynolds stress is decreased, which is mainly a mean density effect. Finally, the growth rate is decreased according to the positive correlation between the growth rate and the Reynolds stress. Moreover, the old momentum thickness definition is no longer appropriate and a new one is introduced specifically for the space-developing LES. The relation between the growth rate and Reynolds stress originally deducted under the time-developing frame is also found to be valid under the space-developing frame.

Topology optimization for fluid field problems has been studied for many years, but most of them use the Eulerian coordinate system in the numerical analysis methods such as the finite element method and the finite volume method. The moving particle semi-implicit (MPS) method is one of the particle methods, which can be used to analyze incompressible free surface fluid flows. The MPS method is a meshless method based on the Lagrangian coordinate system without surface tracking by a mesh or a scalar quantity. It has attracted attention in recent years since this has several advantages such as the easy expression of the free boundaries. This paper presents a new topology optimization method for fluid dynamics problems using the MPS method. First, the optimization problems are formulated based on the level set method and the MPS method. Next, the design sensitivities are derived using the Lagrange multiplier method and adjoint variable method. The optimization algorithm is constructed based on those formulations, and the validity and the availability of the proposed method are confirmed through several numerical examples.

This paper focuses on three-dimensional direct numerical simulations of rising bubbles in the wobbling regime, and the study of its dynamical behavior for Eötvös number 1 ≤ Eo ≤ 10 and Morton number 1e−11 ≤ M ≤ 1e−9. The computational methodology is based on a mass Conservative Level-Set method, whereas the spatial discretization of the computational domain employs an Adaptive Mesh Refinement strategy for the reduction of computational resources. The Navier–Stokes equations are discretized using the finite-volume approach on a collocated unstructured mesh; the pressure-velocity coupling is solved using a classical fractional-step projection method. This methodology is applied to a series of verification and validation tests, which are compared with experiments and numerical results from the literature. Finally, buoyancy bubbles rising in the wobbling regime are researched at moderate to high Reynolds numbers (100

A fractional step lattice Boltzmann method (FSLBM) is developed for incompressible fluid flow in three dimensions. The presented scheme is based on the time-evolution of velocity and pressure in contrast to the evolution of probability density functions. Furthermore, the discretization with coarse corrective steps (CCS) facilitates calculations up to large Reynolds numbers. The method is validated for the friction factor of pipes with various surface roughness, as well as, for the Reynolds stress of smooth pipes. A good agreement is found to general scaling laws and high quality DNS data respectively. Development of turbulent flow in a pipe calculated with ≈ 0.57 × 109 lattice elements on a single GPU is reported. FSLBMs can process 56.6 million elements per GB of GPU memory which is considered a near-optimum memory efficiency for 3D lattice Boltzmann calculations.

International audience; We focus here on a technique to compute compressible fluid flows in physical domains cluttered up with many small obstacles. This technique, referred to here as the integral formulation, consists in integrating the flow governing equations over the fluid part of control volumes including both fluid and solid zones; doing so, the integral of fluxes over solid boundaries may appear, for which expressions as a function of discrete variables must be provided. The integral formulation presents two essential advantages: first, we naturally recover the standard fluid approach when the mesh is refined; second, fluid/solid interactions may be, to some extent, modelled to recover the singular head losses at the interface between a free and a congested part of the computational domain. We apply here this approach to the Euler equations, using a collocated space discretization and a pressure correction algorithm, preserving the positivity of both the density and the internal energy. Verification test cases are performed, including a Riemann problem in a free domain and a shock wave reflection on a wall, using an equation of state whichis suitable for weakly compressible fluid flows. Finally, we address a two-dimensional situation, where a shock wave impacts a set of obstacles; we observe a very encouraging agreement between the integral approach results and a CFD reference solution obtained with a pure fluid approach on a fine mesh.

Two-dimensional flow around a semi-circular profile at the zero angle of attack and at Re = 50000 on the self-oscillatory period is extensively studied by the URANS method involving the standard semi-empirical SST turbulence models, the SST turbulence model with the correction for streamline curvature modified within the Rodi-Leschziner-Isaev and Smirnov-Menter approaches, as well as involving Hanjalic's four-parameter eddy viscosity elliptic relaxation model and its analog - eddy viscosity elliptic blending model proposed in the present work. This has been done with the use of different-structure grids (multiblock with structured overlapping and unstructured composite). Different numerical approximation methods realized in six codes (VP2/3, SigmaFlow, Fluent, CFX, OpenFOAM, and StarCCM+) are used. An underestimation (up to 30%) of time-averaged integral aerodynamic loads is revealed by means of the standard near-wall SST model. This is explained by the high vortex viscosity production in the profile wake. Wind tunnel tests show that the location of cutoff washers on the semi-circular profile provides a quasi-two-dimensional flow around it and allows applying measurement data to verify two-dimensional turbulent flow. The best agreement of experimental results and numerical predictions when comparing the Strouhal number and time-averaged surface pressure coefficient distributions is achieved using both the modified SST model with the correction for streamline curvature and the modified eddy viscosity elliptic blending model. When the SST model with the correction for streamline curvature, modified within the Rodi-Leschziner-Isaev, Smirnov-Menter and Durbin approaches, is used, all the above codes yield close predictions of a vertical aerodynamic load on the oscillation period.

We present an efficient algorithm of a two-dimensional Gas Kinetic Scheme (GKS) suitable for General Purpose Graphics Processing Units (GPGPUs). The algorithm features conservative second order quadtree-type refinement for Cartesian meshes and nested time stepping. The implementation is validated for several incompressible and thermal compressible test cases in the low Mach (Ma) number regime. We find that heat transfer for high Rayleigh (Ra) number and turbulent convection can be simulated correctly. Finally, we demonstrate a simulation of a Rayleigh-Benard setup with R a = 10 13 that qualitatively resembles the conditions of fire on a room scale. The implementation delivers a performance of more than one billion cell updates per second.

A spectrally-accurate algorithm for analysis of the stability of spatially modulated convection has been developed. Modulations can be generated using either geometric, or heating, or both types of irregularities. The algorithm uses a combination of Fourier expansions in the horizontal directions, Chebyshev expansions in the vertical direction and the Immersed Boundary Conditions (IBC) method to capture geometric irregularities. The resulting gridless discretization provides means for an efficient handling of multiple geometries as well as for geometry optimization. Various tests confirm that the algorithm delivers spectral accuracy for the eigenvalues and the eigenfunctions. Examples of applications are provided.

To effectively control the flow over a two-dimensional bluff body, three-dimensional perturbations including spanwise-varying shape modifications and surface actuations have been suggested by previous studies. One of the computational issues is how big the spanwise computational domain size (Lz) should be as compared to the wavelength of these spanwise-varying perturbations (λ), to accurately estimate the effect of these perturbations. To investigate this issue, we consider three different two-dimensional bluff bodies with spanwise periodic perturbations: wavy square cylinder, wavy circular cylinder, and spanwise-varying blowing and suction on a circular cylinder at Re = 100. The spanwise length scales of largest vortical structures existing in the wake significantly depend on Lz, and they are larger than λ, reaching 2λ, 3λ, and even bigger than or equal to 12λ for the cases considered. These largest structures are composed of multiple of elementary vortical structures whose length scales are smaller than or equal to Lz. The amounts of drag reduction by periodic perturbations at Lz > λ are smaller than those at Lz = λ, indicating that the computational domain size equal λ overestimates their performances.

In this paper, a novel flexible forcing immersed boundary-simplified lattice Boltzmann method (FFIB-SLBM) is introduced to efficiently simulate two and three-dimensional fluid-solid interaction problems. Here, the simplified lattice Boltzmann method (Chen et al. [1]) with benefits such as lower virtual memories, ease in the implementation of the physical boundary conditions and higher numerical stability over the standard lattice Boltzmann method is coupled with an implicit flexible forcing immersed boundary scheme (Dash et al. [2]) which accurately satisfies the no-slip condition for the unsteady and moving boundary problems. The proposed FFIB-SLBM solver not only avoids the complex mathematics involved in the large banded matrix inversion but also requires lesser computational memory resources compares to the conventional immersed boundary-lattice Boltzmann method. The capabilities and accuracy of the coupled FFIB-SLBM solver are checked with several two and three-dimensional fluid-solid interaction problems. The obtained results from FFIB-SLBM solver are noticed to be in very good agreement with the published literature.

In this study, a GPU-accelerated improved mixed Lagrangian–Eulerian (IMLE) method is proposed to solve the three-dimensional incompressible Navier–Stokes equations. To improve the prediction accuracy, the proposed IMLE method approximates the total derivative term in Lagragian sense, and the spatial derivative terms are approximated on Eulerian coordinates. Transfer of data from Lagrangian particles to data on Eulerian grids is accurately carried out by adopting moving least squares (MLS) interpolation method. The velocity-pressure decoupling issue is overcome by adopting pressure-free projection method in which the pressure field is calculated by solving a pressure Poisson equation (PPE). It is noted that the MLS interpolation is time consuming since this procedure belongs to a pointwise scheme in which a local matrix equation shall be solved on each grid point. In addition, the discretized PPE forms a large sparse matrix and it is computationally intensive to solve by using the conjugate gradient (CG) method. Therefore, we are aimed to resort to CUDA- and OpenMP-programming means to accelerate the computation. In this study, the performance of the multiple GPUs code can reach up to 27 times faster with respect to multi-threads CPU performance.

Simulations of the flow over a heaving NACA 0012 wing are conducted to study the separated flow phenomena for a pre-stall and post-stall wing condition. An extensively validated high fidelity large-eddy simulation (LES) approach is used to examine the unsteady aerodynamic loads and flow structures at Reynolds number Rec = 2 × 104 based on the chord. We consider reduced frequencies of k = 0.47 and 0.94 for a chord-normalized peak-to-peak amplitude of A/c=0.5 and angles of attack of 5∘ and 15∘, representing pre-stall and post-stall conditions respectively. Comparison to experiment shows good agreement for the phase-averaged lift, drag and moments of the heaving wing. Characteristic phenomena of dynamic stall are analysed with emphasis on the leading edge vortex (LEV) development. A series of instantaneous spanwise vorticity plots show significant spanwise perturbations in the reverse flow region that develops over the suction surface during the start of the downstroke, giving rise to instabilities in the detached shear layer. The instabilities give rise to the first occurrence of turbulence near the wing surface at the leading edge.

Stable and conservative numerical boundary schemes are constructed such that they do not diminish the overall accuracy of the method for interior schemes of orders 4, 6, and 8 using both explicit (central) and compact finite differences. Previous attempts to develop stable numerical boundary schemes for non-linear problems have resulted in schemes which significantly reduced the global accuracy and/or required some form of artificial dissipation. Thus, the schemes developed in this paper are the first to not require this tradeoff, while also ensuring discrete conservation and allowing for direct boundary condition enforcement. After outlining a general procedure for the construction of conservative boundary schemes of any order, a simple, yet novel, optimization strategy which focuses directly on the compressible Euler equations is presented. The result of this non-linear optimization process is a set of high-order, stable, and conservative numerical boundary schemes which demonstrate excellent stability and convergence properties on an array of linear and non-linear hyperbolic problems.

The shock wave/boundary-layer interaction of chemically reacting flow in a shock tube is studied using a high-order point-implicit solver. The solver employs a high-resolution weighted essentially non-oscillatory (WENO) scheme to capture the complex shock structures, together with a point-implicit method to overcome the stiffness of the chemical production term in the multicomponent Navier–Stokes equations. The numerical code is carefully validated with three benchmark tests, which demonstrates the robustness and good performance of the combined numerical methods. The unsteady interaction process between the shock wave and boundary layer in a two-dimensional shock tube is clearly captured with detailed flow patterns in the simulation. Simulation results show that regular vortex arrangements appear in the flow field for the case of Mach number 2.37, while for the case of Mach number 3.15, the vortex structures break up and chemical nonequilibrium effects become apparent. The influence of real gas effects on shock wave/boundary-layer interaction is further identified on the temperature field and triple point trajectory.

The present paper studies the effect of particle density in a turbulent channel flow laden with resolved oblate spheroids at a frictional Reynolds number of Re τ = 180 . Direct numerical simulations are performed by using the lattice Boltzmann method (LBM) for solving the flow field. Particle-fluid interactions are modeled by the immersed boundary method (IBM). Simulations are done for dense regimes of heavy and neutrally-buoyant particles with a volume fraction of 5%. The particle-fluid density ratios are 8.0 and 1.0 for heavy and neutrally-buoyant particles, respectively. Results show that particle inertia can significantly modify the fluid and particle statistics. Heavy particles cause a higher reduction of the fluid streamwise velocity with respect to the single-phase flow. Turbulence is attenuated by both particle types but the reduction is stronger with heavy particles than that with neutrally-buoyant ones. Moreover, increasing the density of particles is found to create smaller but more energetic vortices. Quadrant analysis shows that the contribution of ejection and sweep events in the Reynolds shear stress reduce on increasing the particle density. The local volume fractions of the two particle types are also seen to be different. While the volume fraction of neutrally-buoyant particles reach a constant value at a certain distance from the walls, the concentration of heavy oblate spheroids increases gradually all the way up to channel center. Both particle types show preferential orientation near the walls, where the symmetry axis is normal to the wall. However, this preferential orientation is less pronounced when increasing the particle inertia. Finally, the translational velocity fluctuations of heavy particles are found to be higher in the streamwise direction, but lower in the wall-normal direction.

The question of whether it is possible to set relevant, robust and reliable benchmarks for viscous free-surface flows with complex free-surface dynamics is investigated in this work. The proposed method for finding an answer to this question consists of selecting three conditions leading to increasing flow complexity and to simulate them using three well established solvers based on diverse numerical techniques. In the three conditions, a submerged horizontal cylinder in an uniform current perpendicular to its axis is considered, the Reynolds number is fixed to 180, and the analysis is limited to a 2D framework. While the unbounded solution for such flow is well established, adding a free surface and setting the submergence ratio and the Froude number in certain ranges, challenging free-surface dynamics takes place. In the specific conditions selected, phenomena of increasing complexity are identified and studied with: (i) δ + -SPH, an enhanced version of the Smoothed Particle Hydrodynamics method, (ii) a single-phase Finite Volume scheme with a Level Set function for tracking the free-surface (LS-FVM), and (iii) a two-phase Finite Volume with a Volume-of-Fluid algorithm to treat the gas/liquid interface (VOF-FVM). It is shown that the test-cases, even being geometrically simple, present intricate complexities, such as alternate metastable states in the wake, linked to the strong non-linearities induced by the interactions between the wake’s vorticity and the free surface. It is also shown that the solvers considered are able to depict a consistent representation of these complex flows, useful as benchmarks for other solvers and methods. An additional research question, investigating whether the improvements of the δ + variant of the SPH method are necessary for simulating specific aspects of the flows treated in the paper, is also posed and discussed.

Low-speed rarefied gas flow in a lid-driven cavity is chosen as a test case in order to assess the accuracy and efficiency of both the Direct Simulation Bhatnagar-Gross-Krook (DSBGK) method and the Discrete Velocity Method (DVM) for solving the BGK kinetic equation. Various lid-speeds and a broad range of rarefaction levels, from slip to near free-molecular flows, are investigated. The DSBGK and DVM results are in satisfactory agreement for all the examined cases in 2D and 3D. As a statistical method, the stochastic noise of the DSBGK method is much smaller than that of the conventional Direct Simulation Monte Carlo (DSMC) method, and is independent of the Mach number. To achieve the required accuracy, the DSBGK simulations need more CPU time than the DVM simulations, i.e. for the 2D cases, a factor of 2 to 15 times more for convergence, and about 50 to 80 times more overall, including the time-averaging process. However, for 3D cases, the third direction in the DVM velocity grid is needed, so the computational cost of DSBGK is now only 0.16 to 0.51 times that of the DVM for the convergence process, and 1.6 to 5.8 times that of the DVM overall. The efficiency of the DSBGK method can also be expected to be enhanced in large-scale 3D simulations, where the computational cost for time-averaging becomes negligible in comparison with the convergence process. The DSBGK simulations require much less memory, even at low Mach numbers, than the DVM simulations; in the test cases with the required accuracy, about 10 simulated molecules per cell in the DSBGK simulations are sufficient for an arbitrary Kn, while the DVM requires at least 4 × 24 and 4 × 24 × 12 velocity grids for the 2D and 3D cases, respectively, even at Kn = 0.1 . Finally, we discuss the ray effects in the DVM, which exist in flow problems with a discontinuous boundary and are caused by incompatibility of the velocity grid, the spatial grid, and the order of accuracy of the numerical scheme.

The turbulent airflow in 2D and 3D channels with bends of opposite walls is studied numerically. The channels are slightly divergent in the longitudinal direction upstream and downstream of the bends. The flow is supersonic on the inlet and outlet boundaries of the computational domain. Solutions of the Reynolds-averaged Navier–Stokes equations are obtained with a finite-volume solver of second-order accuracy. The solutions demonstrate considerable hysteresis under variations of the free-stream Mach number or angle of attack. At the ends of hysteresis bands, the flow structure changes drastically due to instability of shock wave positions. Effects of 3D phenomena, turbulent viscosity, and thickness of walls on the hysteresis are discussed.

An implicitly coupled pressure–velocity transient scheme for the solution of the Eulerian multi-fluid model with any number of phases (MIC) was developed and implemented in OpenFOAM®. The numerical methodology is based on the phase-intensive momentum equations for the phase velocities and a pressure equation using a deferred-correction approach of the Rhie–Chow interpolation. An extension of the compact momentum interpolation method (CMI) to a system with any number of phases was developed. The developed methodology was tested against a segregated multiphase solver (MS) and a steady-state single phase solver, in cases considering up to four phases. The proposed method has proven to be more robust and accurate than the segregated counterpart, being able to converge in cases with large drag coefficients, providing time-step independent steady-state solutions.

An improved ghost-cell immersed boundary method coupled with a high-order finite difference scheme is currently proposed to numerically simulate the reflected shock/boundary layer interaction in a wavy-wall tube. The main improvement of current algorithm involves the particular treatment of the solid boundary reconstruction procedure by using both ghost points in solid domain and forcing points in fluid domain together. Owing to this kind of improvement operation, the amount of points used to recover the solid boundary increases greatly and will inevitably promote the accuracy of solid boundary reconstruction, which will play a significant role in the current high-order accurate numerical simulation. A typical validation case of 2-dimensional shock/circular cylinder interaction is conducted and demonstrate that the current improved numerical method can be used to capture the flow details such as shock bifurcation and small vortex very well and improve the numerical precision greatly. The improved method is then applied to numerically investigate the effects of boundary layer on the propagation of the shock in a wavy-wall tube. It is observed that, at low Mach number, the existence of boundary layer has little effect on the shock propagation. As the Mach number increases to 1.9, some certain complicated flow features will occur due to the enhanced boundary layer effects. In the early stage, the flow structures are nearly the same as those without the boundary layers. In the transition stage, a high-speed shear band behind the leading shock is observed and finally evolves into a worm-like structure, whose instability is illustrated by qualitative assessment on its flow features. In the developing stage, a remarkable shock bifurcation phenomenon is present and the worm-like structures will start shedding regularly, which will induce a series of scattering-like waves and asymmetrical flow fields. These characteristics demonstrate that the bifurcated shock waves located in upper and lower walls of the wavy-wall shock tube act as a primary trigger to gradually destabilize the shocked flow.

The prediction of separation bubbles is highly important due to the controlling effects that they have on the airfoils performance. In the present study, a two-dimensional numerical simulation of the incompressible transitional flow around the NACA 0012 and Eppler 387 airfoils is studied. In order to examine the capability of the turbulence models for predicting the separation bubbles, several modified versions of the three-equation k-kL-ω turbulence model presented in previous research studies and the original four-equation SST k-ω turbulence model are compared with the experimental and Direct Numerical Simulation (DNS) data. A new modification based on the previous modified versions of the k-kL-ω model is also proposed. The Reynolds number based on the airfoil chord length is between 3 × 104 and 1.3 × 105. Simulation of the flow-field is performed by the solution of the Reynolds-averaged Navier–Stokes equations using a pressure-velocity coupling algorithm so-called RK-SIMPLER. An explicit method of second-order accuracy in time and space is used to integrate the momentum conservation equations. The results from this study indicate that the new proposed modification presents the better prediction for the separation bubbles than the previous versions, especially in the long separation bubbles. An excellent result is also obtained for the lift coefficients.

This paper serves to simulate compressible multi-fluid flows using an energy-splitting method based on the generalized Riemann problem (GRP) solver. The emphasis is put on two-dimensional problems to address the fundamental role of transversal effect in the construction of numerical fluxes, which exhibits the genuine multi-dimensionality of the underlying numerical schemes. In contrast with the popularly-used methods of line which use exact or approximate Riemann solvers, the GRP solver, as the discontinuous version of the Lax–Wendroff method, takes the temporal-spatial coupling process to include the transversal effect. Combined with the energy-splitting technique developed earlier in Lei and Li [24], the resolution of flow fields around material interfaces is improved significantly.

In this work, an efficient approach for quantifying the parameter uncertainty for expensive computer models is proposed, which combines the high dimensional model representation (HDMR) technique and the Gaussian process machine learning (GPML) method to construct the surrogate model, then the so-constructed surrogate is used in the Bayesian inference procedure to obtain the posterior distribution of the model parameters. The applications of the proposed approach to simple mathematical functions are investigated, demonstrating its efficiency and accuracy for both continuous function and function with discontinuities. The computer design of the sampling points based on GPML is also proposed and the results show that the proposed method is promising in terms of both efficiency and extensibility to high dimensional problems. After testing the proposed approach with simple mathematical functions, it is applied to the two equation SST turbulence model for hypersonic flow over flat plate with a wide range of Mach numbers. A Bayesian scenario-averaging method based on the flow quantities that can characterize both the flow scenario and the model’s performance in the scenario is proposed and it is employed for the model predictions of new flow scenarios. The results show that the prediction mean values match well with the DNS data and the corresponding uncertainties are well captured.

Minimum-dissipation sub-grid models represent simple alternatives to the Smagorinsky-type approaches to the implementation of sub-grid scales’ (SGS) effects in the large-eddy simulation (LES) approach. Recently, the anisotropic minimum-dissipation (AMD) model has been introduced, which is a static type of eddy-viscosity SGS model and is a new addition to this family. This model is easy to implement; furthermore, not only can it consider the effect of various directions in computing sub-grid stress, it can also operate transitional flows from laminar to turbulent. For the first time, we implemented AMD in the open source package OpenFOAM. Foremost, we verified the OpenFOAM implementation of the AMD model for the prediction of isotropic decaying turbulence, a temporal mixing layer and an internal channel flow. To achieve this, decaying turbulence was considered for the isotropic turbulence produced by a grid with a mesh size of 5.08 × 10–2 m in a flow of mean velocity of 10 m/s. The temporal mixing layer was simulated at a Reynolds number based on half the initial vorticity thickness of 105. Channel flow was investigated at the three frictional Reynolds numbers of 180, 395 and 590. The verification results revealed that the implemented AMD model in OpenFOAM offered satisfactory accuracy to capture decaying turbulence and temporal mixing layer and calculate boundary layer velocity profiles and first and second-order turbulent parameters in the channel flow on anisotropic grids. Following this, for the first time, we evaluated AMD's performance in predicting external non-cavitating and cavitating flows over a 3D sphere. Non-cavitating and cavitating flow over the sphere were considered at Re = 2 × 104 and Re = 1.5 × 106, respectively. The AMD results were then compared with the direct numerical simulation (DNS) data and the numerical results obtained from the established SGS models such as dynamic Smagorinsky (DS), one equation eddy viscosity model (OEEVM), detached eddy simulation (DES), and delayed detached eddy simulation (DDES), where applicable. In treating sphere flow, in spite of the use of a coarse grid rather than the alternative SGS models, the AMD model predicted accurate results for pressure coefficient, shear stress, and separation point location over the sphere as well as the velocity profile in the wake region. It was detected that the simulation time of the AMD model was lower than that of DS in all the considered test cases by approximately 10–16%.

To treat the problem of low aerodynamic performance and high unsteadiness of a flow around an airfoil at low Reynolds numbers, passive actuation techniques have been used. A NACA0012 airfoil at Re = 103 and high incidence angles (15° and 20°) equipped with a trailing edge and/or extrados flexible flaps has been studied. The two-way Fluid-Structure Interaction has been studied by coupling the “CFD-Fluent” and “Transient Structural” systems in the ANSYS-Workbench 15.0 software. A reduced order model of the lift coefficient oscillation based on the van der Pol oscillator has been formulated. The analytical model helps analyze and understand the underlying physics of the nonlinear system. The characteristics of the limit cycle oscillation of the lift coefficient have been modified by decreasing the amplitudes proportional to the principal and second Strouhal numbers and by increasing the amplitude proportional to the third Strouhal number. These modifications are influenced by the interaction between the detached flexible flap and the trailing edge vortex downstream of the airfoil, which provokes the change in the flow topology. It has also been shown that the presence of the trailing edge flexible flap has the effect of increasing the lift coefficient and reducing the unsteadiness coefficient.

We present a detailed analysis of experimental and numerical results for the flow of trailing vortices behind a NACA0012 wing model. Particular attention is paid to a specific value of the angle of attack, α=9°, and ultra-low and low chord-based Reynolds numbers ranging from Re=3 × 102 to 2 × 104. Spatial-averaged two-dimensional Particle Image Velocimetry (PIV) velocity profiles are in agreement with implicit Large Eddy Simulations (iLES) up to eleven chords from the wing for Re=7 × 103. Once we validate our numerical results through experiments, we fit the theoretical parameters such as normalized circulation (S, b), vortex decay exponent (n) and virtual origin ( z ¯ 0 B , z ¯ 0 M S ) as a function of Re. Thus, five theoretical parameters are given from computational and experimental results: two corresponding to Batchelor’s model (S, z0B) and three belonging to Moore & Saffman’s model (b, n, z0MS). Two critical Reynolds numbers were found. Our computations verify that the onset of wake instability at the first threshold ReC1 ≈ 1.3 × 103 captures the change in the trend of theoretical parameters. In addition, the theoretical parameters appear to become constant experimentally for a second critical Reynolds number ReC2 greater than 1–2 × 104 when our results are compared with those given by other authors. Consequently, Reynolds number plays an essential role in the stability analysis for trailing vortices, not only taking into account viscous terms but also determining the input parameters for theoretical models.

A novel subgrid closure model is proposed for performing Large Eddy Simulation (LES) of turbulent compressible flows with block structured Adaptive Mesh Refinement (AMR) strategy. The new approach, henceforth called as AMRLES, is an improvement over the well-established one-equation based subgrid turbulent kinetic energy model with corrections proposed to consistently handle the total resolved turbulent kinetic energy across a multi-level AMR grid hierarchy. The proposed correction for the subgrid kinetic energy is based on an explicit on-the-fly filtering operation from finer grids to underlying coarser grids. The effect of the inter-grid correction is demonstrated by investigating advection of decaying isotropic turbulence across a coarse/fine and fine/coarse AMR grid interface. In the case of fine-to-coarse transition, the multi-level model is shown to correctly recover the subgrid turbulent kinetic energy. AMRLES is then applied to study the canonical problem of shock turbulent interaction. Two different Reynolds numbers are considered and the behavior of the inter-grid corrections on the subgrid turbulent kinetic energy and the subgrid turbulent stresses are analyzed for both the cases. Comparison with filtered DNS results indicates that AMRLES is able to predict the behavior of turbulent statistics across the shock in a satisfactory manner.

A novel multi-phase flow formulation using a level-set-based interface-capturing approach is proposed, focusing on addressing numerical challenges associated with the modeling of surface tension. The surface tension is handled through the continuum surface force model. The residual-based variational multiscale (RBVMS) formulation is employed to solve the coupled Navier–Stokes and level-set convection equations. The RBVMS formulation is discretized using either standard low-order finite elements, or Isogeometric Analysis (IGA) based on Non-Uniform Rational B-Splines (NURBS), which are higher-order accurate and smooth. The proposed method is applied to the simulation of 3D bubbles moving in viscous liquids with large density and viscosity ratios representative of common two-phase flow systems. The accuracy of the proposed method is assessed by comparing the results with analytical solutions, experimental data, and computational results, reported in the literature. In all cases IGA showed superior performance to standard finite elements; this superiority is attributed to the higher-order accuracy of IGA and its ability to directly and accurately compute, using smooth NURBS functions, the curvature term, which is a key ingredient the surface tension formulation. For single-bubble rising problems, the proposed approach produced accurate predictions of the terminal bubble shape, velocity and Reynolds number. The advanced nature of the new multi-phase flow formulation is demonstrated with a simulation of merging of two bubbles in the presence of a deforming free-surface.

We propose a low-Mach correction for cell-centered schemes in Lagrangian frame. After transposing some classical results from the Eulerian frame to the Lagrangian frame, we show why classical cell-centered Lagrangian schemes are not able to capture the low-Mach regime except by using unreasonably fine meshes. Consequently, we propose a slight modification of the original scheme, which is easy to implement in any scheme using an acoustic Godunov solver on unstructured mesh, and has a negligible cost in term of CPU time. We demonstrate that this modification cures this flaw. The properties of the original semi-discrete scheme (consistency, conservation) are preserved. Particular attention is paid to the entropy condition, proving its compatibility with the proposed modification. We assess this new scheme on several low and high-Mach problems, to demonstrate its good behavior in all regimes. Our last test problem is devoted to the study of the growth rate of instability in convergent configurations. It shows that even if the problem is globally very compressible, the low-Mach correction can have a significant impact on the solution.

The effect of passive flow control using an oscillating micro-cylinder near the leading edge of a stalled airfoil (S809) at a Reynolds number of 1 × 106 is numerically investigated. A physical analysis of the flow fields is performed to illustrate the mechanisms of flow control for the improvement of airfoil aerodynamic performance. When the optimal parameters are selected, the research about the ability of suppressing the separation of the static micro-cylinder is studied at different angles of attack. The simulation results show that the static micro-cylinder can effectively suppress the flow separation and improve the aerodynamic performance of airfoil at angles of attack range from 10° to 24°. Then we replaced the static micro-cylinder with the oscillating one. The simulation results proved that when a static micro-cylinder cannot control the flow separation well, a better flow control effect can be achieved by the oscillating cylinder. Furthermore, the diameter of the oscillating micro-cylinder is smaller than the static one's when a same lift-to-drag ratio is achieved. Compared with the original S809 airfoil, the lift-to-drag ratio of the airfoil with an oscillating micro-cylinder can be increased by 88.21% at optimal oscillate method.

A Cartesian grid-based, immersed-boundary method combined with a moving domain is used to simulate sphere and oblate spheroid settling under gravity. For the moving domain, grids are generated or deleted based on the location of the object centroid, ensuring a constant size of the computational mesh. Sphere settling under gravity is first simulated, and the predicted drag coefficients at different Reynolds numbers, that is, 4.1 to 2000, agree reasonably with measurements. Finally, an oblate spheroid descending under gravity is further simulated with Reynolds numbers at 44.5 to 1617. For the Reynolds numbers examined, the motions are two-dimensional, and the fluttering motions exist in all the Reynolds numbers investigated except at Re = 44.5, in which steady falling prevails. This is consistent with previous investigations for falling disks, where the threshold for the steady and fluttering motion is at around Re = 80 for the level of moment of inertia investigated. As the spheroid flutters, different vortex branches are generated in the trailing edge direction, in which hairpin-like vortices occur.

Present work is an extensive numerical investigation of interfacial flow in 5 cSt silicone oil that develops under the action of thermo-capillary force and interaction of this flow with the surrounding air motion using the commercial software ANSYS Fluent 17.2. The physical model is a half floating zone of high Prandtl number fluid (Pr = 56) co-axially surrounded by ambient air under microgravity conditions. The surface of a slender liquid bridge (VR = 0.9) is subjected to parallel air stream which is co-directed and counter-directed with the thermo-capillary flow along the interface. This forced air motion influences the basic flow in the system via shear stress and heat transfer at the interface. The effect of ambient air velocity and the volume ratio of the liquid bridge on the evolution of flow states is examined by performing axisymmetric computations in both liquid and air domains. The considered values of air velocity are comparable or larger than the Marangoni velocity to account for the shear action employed by the parallel airflow. The results show that the heat loss at the interface characterized in terms of local Biot number is significantly higher in case of counter-directed airflow as compared to that of co-directed airflow. By varying the volume ratio of the liquid bridge (0.90

We present an improved phase-field model in the lattice Boltzmann scheme to investigate the droplet dynamics in the presence of soluble surfactant. The phase-field model based on the Ginzburg–Landau free energy is developed in which the immiscible binary fluid interfacial profile is independent of the surfactant concentration. The improved model is validated and then employed to study the surfactant effect on single droplet deformation, two droplets interactions and interactions among four droplets in the shear flow. The results show that the increase of surfactant concentration promotes droplet deformation, droplet breakup and more complex droplet-droplet interaction compared to the clean droplet. Moreover, the effects of capillary number, viscosity ratio, as well as peclet number on the behavior of surfactant-covered droplets in the shear flow are investigated. The results indicate that the droplet Taylor deformation parameter increases with the increase of capillary number but the decrease of viscosity ratio. The minimum distance between two interacting droplets enlarges with both capillary number and peclet number.

An unsteady Reynolds-averaged Navier–Stokes (URANS) model coupled with an immersed-body method is used to model fluid-structure interaction (FSI) for moderate Reynolds number flows. Particular attention is paid to the application of suitable flow boundary conditions with the immersed-body method. This model couples a combined finite-discrete element solid model and a finite element fluid model with the standard k − e model. A thin shell mesh surrounding the solid surface is first used as a delta function to apply the interface boundary conditions for both the URANS model and the momentum equation. In order to reduce the computational cost, a log-law wall function is used within this thin shell to resolve the flow near the solid wall. To improve the accuracy of the wall function, a novel shell mesh external-surface intersection approach is introduced to identify sharp solid-fluid interfaces. More importantly, an unstructured anisotropic mesh adaptivity is used to refine the mesh according to the interface and the velocity, which improves the accuracy of this immersed-body URANS model with use of a limited number of fluid cells. This immersed-body URANS method is validated by several test cases and results are in good agreement with both experimental and numerical data from the literature.

As a Lagrangian meshless method, moving particle semi-implicit (MPS) method has been proven useful in the analysis of the free-surface flow, especially accompanied by the large deformation and fragmentation of fluids. The improvement of pressure distribution in three dimensions is an important aspect to verify the effectiveness of MPS. The accurate representation of 3-D geometries especially complex geometries is the premise of obtaining convincing pressure distribution. However, most of MPS applications cannot accurately represent complex wall geometries, which highly affects the reliability of MPS. For this reason, the triangle meshes are used to accurately represent the complex wall geometries in this research. The polygon wall boundary condition (PW) is adopted to enforce the wall boundary condition to the triangle meshes. The pressure of the wall boundaries is derived from the Neumann boundary condition to improve the velocity distribution of fluid particles near the wall boundaries. A first-order gradient model is presented to improve the accuracy and stability of the PW. Our approach can enhance the numerical stabilization to arbitrary geometries. We simulate several 3-D examples such as the classic hydrostatic simulation and the complex 3-D geometries with sharp angles and curved surfaces to demonstrate the general applicability of our new model.

It is convention in computational mechanics to use Eulerian grids for fluids and Lagrangian grids for solids. In this paper, a novel method called ELL using both Lagrangian and Eulerian grids for fluids is presented in a carefully designed manner to handle complex fluid–structure interaction (FSI) problems with moving thin rigid body. The key idea is to use a small portion of the fluid to wrap the thin body. This wrapping fluid is described in Lagrangian coordinate, the same way the solid is described. They are treated as one “composite solid” thus the immersed domain method (IDM) can be implemented. In this way, the moving interface boundary conditions can be explicitly imposed with the help of the unified Lagrangian grids in the interaction zone. The initial fluid domain can still be treated as usual Eulerian grids based on IDM theory by introducing a fictitious fluid. The FSI interface can be accurately modeled since the wrapping fluid and the solid are always attached together. This effectively solves the major “blur interface” problem in the conventional immersed boundary method (IBM). To demonstrate this ELL idea, a number of benchmark examples have been studied in comparison with the results in the open literature. Finally, a 2D flapping wing is simulated to show the potential of ELL in engineering application. It is observed that ELL method proves to be good in performance.

The paper proposes second-order accurate direct Eulerian generalized Riemann problem (GRP) schemes for the radiation hydrodynamical equations (RHE) in the zero diffusion limit. The difficulty comes from no explicit expression of the flux in terms of the conservative vector. The characteristic fields and the relations between the left and right states across the elementary-waves are first studied, and the exact solution of the 1D Riemann problem is then gotten. After that, the direct Eulerian GRP scheme is derived by directly using the generalized Riemann invariants and the Rankine–Hugoniot jump conditions to analytically resolve the left and right nonlinear waves of the local GRP in the Eulerian formulation. Several numerical examples show that the GRP schemes can achieve second-order accuracy and high resolution of strong discontinuity.

A novel formulation for the diffusive term in the continuity equation is proposed to improve the stability of smoothed particle hydrodynamics weakly compressible scheme avoiding the introduction of empirical parameters. Densities at particle-particle interface have been computed by means of a first-order consistent total variational diminishing reconstruction and a one-dimensional Roe’s approximate Riemann solver is applied to add the correct amount of diffusion. Results of numerical tests also demonstrate that the proposed method is able to guarantee consistency both inside the fluid and close to the free surface. Furthermore, a numerical analysis of several flux limiter functions has been conducted, finding that the choice of this function is a critical point to guarantee the accuracy of the method. It has been assessed, through the monitoring of the internal energy, that the van Albada limiter is more effective in dissipating spurious density fluctuations.

In this paper Eulerian weakly compressible SPH (EWCSPH) is coupled to the Vector-based discrete element model (V-model) to produce a robust mesh-less SPH-V model for fluid-structure interaction (FSI) applications including thin highly flexible bodies. The V-model, originally proposed as a model for granular structures, is extended herein to model non-linear deformation of a continuum representation of elastic structures. Non-linear static validation tests show that the extended V-model provides an accurate representation for problems involving large deformation. Undamped free vibration tests show the V-model is also accurate for transient problems. The SPH-V model with the immersed boundary method and SPH of Eulerian weakly compressible form is applied to established FSI tests for validation. These are oscillation of a flexible plate in quiescent fluids and flow past a cylinder with a rigidly connected flexible flat plate. The complex flow through flexible valve leaflets representative of flow through deep leg veins is demonstrated. Results thus show the SPH-V model is able to accurately capture complex flow features and also non-linear structural mechanics in fully coupled FSI problems.

The development of Lorentz force and its directional effect on the free convection flow and heat transfer in a cube are studied numerically under the influence of a magnetic field using the open source CFD tool kit OpenFOAM. The vertical opposite sidewalls are kept as isothermal while other walls are maintained as insulated. The considered working range of Rayleigh number (Ra) is 104, 106, and 108 at fixed Prandtl number (Pr) of 0.71. The effect of the orientation and intensity of applied magnetic field in the direction normal (Bx) and parallel (By) to the isothermal surface are reported. It is noticed that the distribution of electric potential, the nature of the flow of the electric current and the strength of the Lorentz force varies with the intensity of the magnetic field and its orientation. The hydrodynamic and thermal boundary layers get thinner with the increase in Ra, and the Nusselt number increases in natural convection flow cases. The induced Lorentz force significantly suppress the fluid movement and consequently heat transfer. The damping of fluid motion and convective heat transfer are more in case of Bx magnetic field compared to By field. The detail discussion on the development of Lorentz force and its strength with the direction in the domain is reported. The temperature distribution and iso-surface shows the significance of applied magnetic field on the mode of heat transfer.

The goal of this study is to develop an efficient numerical algorithm applicable to a wide range of compressible multicomponent flows, including nearly incompressible low-Mach number flows, flows with strong shocks, multicomponent flows with high density ratios and interfacial physics, inviscid and viscous flows, as well as flows featuring combinations of these phenomena and various interactions between them. Although many highly efficient algorithms have been proposed for simulating each type of the flows mentioned above, the construction of a universal solver is known to be challenging. Extreme cases, such as incompressible and highly compressible flows, or inviscid and highly viscous flows, require different numerical treatments in order to maintain the efficiency, stability, and accuracy of the method. Linearized block implicit (LBI) factored schemes (see e.g. Briley and McDonald, 1980 [1], Beam and Warming, 1978 [2]) are known to provide an efficient way of solving the compressible Navier–Stokes equations (compressible NSEs) implicitly, allowing us to avoid stability restrictions at low Mach number and high viscosity. However, the methods’ splitting error has been shown to grow and dominate physical fluxes as the Mach number approaches zero (see Choi and Merkle, 1985 [3]). In this paper, a splitting error reduction technique is proposed to solve the issue. A shock-capturing algorithm from [4] is reformulated in terms of finite differences, extended to the stiffened gas equation of state (SG EOS) and combined with the LBI factored scheme to stabilize the method around flow discontinuities at high Mach numbers. A novel stabilization term is proposed for low-Mach number applications. The resulting algorithm is shown to be efficient in both low- and high-Mach number regimes. Next, the algorithm is extended to a multicomponent case using an interface capturing strategy (see e.g. Saurel and Abgrall, 1999 [5]) with surface tension as a continuous surface force (see Perigaud and Saurel, 2005 [6]). Special care is taken to avoid spurious oscillations of pressure and generation of artificial acoustic waves in the numerical mixture layer. Numerical tests are presented to verify the performance and stability properties for a wide range of flows.

An essential step in adjoint-based aerodynamic shape optimization is to obtain the Lagrange multiplier by solving a sparse linear adjoint system of equations based on the Jacobian matrices from the converged flow states. Such an approach has been applied widely within the aerospace community for the design of aircraft and other optimization problems for aerospace applications. However, the need to resolve the flow over complex geometries often requires highly stretched grids and gives rise to anisotropic flow fields which increase the stiffness of the discrete Jacobian needed for the solution of the adjoint system. When a GMRES algorithm preconditioned by an Incomplete LU factorization is used, this stiff linear system requires the use of a large number of Krylov subspace vectors and a high level of fill-in; both require an increase in the amount of memory. Deflated restarting, which distributes spectral eigenpairs, has proven to be an effective method to enhance the convergence rates when solving an ill-conditioned linear system of equations. In this paper, we propose an algorithm to dynamically determine the number of deflated vectors and to deactivate deflation to reduce memory utilization. We demonstrate its efficiency for a two-dimensional NACA 0012 airfoil, the three-dimensional Common Research Model (CRM) wing, and two three-dimensional complete aircraft configurations in viscous flow.

The Finite Volume Particle Method (FVPM) is a meshless method that incorporates features of both Smoothed Particle Hydrodynamics and the Finite Volume Method. Here, two new formulations are presented which enhance its performance in simulation of free surface flows. One is a method for determining the velocity of the free surface, making use of a partial Riemann problem to analyse the flow between the particle barycentre and the geometric free surface. The second is a well-balanced formulation for gravity forces that enables hydrostatic equilibrium to be preserved exactly. Results are presented for hydrostatic, 1D impact, dambreak and deep-water standing wave test cases. Computations display convergence and good agreement with experimental data. The new methods recover exact hydrostatic equilibrium, improve robustness and reduce acoustic pressure fluctuations in dambreak flows, and reduce dissipation. (C) 2018 Elsevier Ltd. All rights reserved. peer-reviewed 2020-10-04

In this paper, we construct a new seventh-order finite volume compact weighted essentially non-oscillatory (WENO) scheme for solving one and two dimensional hyperbolic conservation laws. We extend the main idea of fifth-order finite volume compact-WENO scheme which comes from the original WENO schemes to construct the present seventh-order scheme, where fourth-order compact stencils will be combined with nonlinear weights to get seventh-order finite volume compact-WENO scheme. The parametrized maximum principle preserving flux limiter is coupled with the seventh-order compact-WENO scheme for solving scalar hyperbolic conservation laws and the parametrized positivity satisfying flux limiter is applied to the new scheme for solving compressible Euler equations to maintain positive density and pressure. The HLLC (Harten, Lax and van Leer) flux function is used to compute the interface fluxes in the finite volume formulation. A number of 1D and 2D numerical tests are performed to demonstrate the efficiency and high-resolution properties of the proposed high-order compact scheme.

The flow through a thin slit and a thin orifice is studied with the Direct Simulation Monte Carlo (DSMC), cubic Fokker–Planck (FP), and a coupled FP-DSMC hybrid method. Pressure driven monatomic gas flows through a slit and an orifice with various values of degree of rarefaction and pressure ratio are computed. The DSMC method is physically accurate for all flow regimes; however it is computationally expensive in high density, near continuum regions. An alternative stochastic particle scheme, the cubic FP kinetic model has addressed this issue by approximating the particle collisions involved in the Boltzmann collision integral with continuous stochastic processes. The ability of the cubic FP method to reproduce breakdown of translational equilibrium is discussed. In addition, a coupled FP-DSMC hybrid scheme is employed aiming at an efficient and accurate solution. The FP-DSMC hybrid scheme employs DSMC in rarefied regions and FP method in near continuum flow regions. Numerical procedures of the cubic FP method are implemented within the framework of an existing DSMC-solver, SPARTA. The FP-DSMC hybrid solution reproduces pure DSMC solution with improved computational efficiency up to a factor of eight for vacuum flow through a thin slit.

“Smoothed particle hydrodynamics” (SPH) is a particle method that becomes increasingly popular in different fields of science and engineering. Reason for the popularity are the different advantages in comparison to conventional grid-based computational fluid dynamics (CFD). One example is the much cheaper identification of ”Lagrangian coherent structures” (LCS) in fluid flows by means of the “finite-time Lyapunov exponent” (FTLE). Schemes for the evaluation of FTLE fields based on SPH datasets already exist. Despite the smaller computational effort required in case of SPH data, their evaluation is still costly. This may be the reason that no investigations have been published presently which address the application of existing schemes to SPH-data in 3-D. Therefore in the current paper a new and highly efficient GPU implementation of an existing scheme for the evaluation of FTLE fields is proposed that enables the interactive analysis of large SPH datasets. The suitability of the scheme in case of 3-D datasets and the computational efficiency of the novel GPU implementation are demonstrated. Furthemore, the so called particle birthtime is presented as a cheap alternative to FTLE fields, even though it has a variety of limitations compared to FTLE fields.

To impose boundary conditions, data at the boundaries must be known, and consequently measurements of the imposed quantities must be available. In this paper, we consider the two most commonly used inflow boundary conditions with available data for internal flow calculations: the specification of the total temperature and total pressure. We use the energy method to prove that the specification of the total temperature and the total pressure together with the tangential velocity at an inflow boundary lead to well-posedness for the linearized compressible Euler equations. Next, these equations are discretized in space using high-order finite-difference operators on summation-by-parts form, and the boundary conditions are weakly imposed. The resulting numerical scheme is proven to be stable and the implementation of the corresponding nonlinear scheme is verified with the method of manufactured solutions. We also derive the spectrum for the continuous and discrete problems and show how to predict the convergence rate to steady state. Finally, nonlinear steady-state computations are performed, and they confirm the predicted convergence rates.