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The numerical prediction of two-phase flows with an interface is challenging, to a considerable extent because of the high density ratio at the interface. Numerical results become affected by momentum losses, diverging spurious interface velocities, free surface distortion, and even numerical instability. To prevent issues like these, consistent momentum and mass transport with an additional continuity equation were introduced. In this article, we describe how a consistent discretization was incorporated into our own method and extended for fluid-structure interaction (FSI) with moving rigid bodies. The new method was tested against benchmark simulations from literature confirming that consistent transport modeling gives a significant improvement compared to non-consistent modeling for the dynamics of two-phase flows. Newly devised proof of principle FSI simulations with momentum transfer from fluid to body in the presence of a high-density ratio between fluids are introduced that could serve as a benchmark for future studies. The simulations demonstrate that consistent modeling gives an order of magnitude improvement in terms of momentum conservation compared to non-consistent modeling. Simulations with the new method are also compared to FSI experiments from literature. Results obtained with the consistent method are closer to the measurements than results of the non-consistent method. The merit of consistent modeling with and without FSI becomes especially apparent for two-phase flows with a high-density ratio between fluids.

The international tokamak ITER is progressing towards assembly completion and first-plasma operation, which will be a physics and engineering challenge for the fusion community. In the preparation for ITER experimental scenarios, non-linear MHD simulations are playing an essential role to actively understand and predict the behaviour and stability of tokamak plasmas in future fusion power plant. The development of MHD codes like JOREK is a key aspect of this research effort, and provides invaluable insight into the plasma stability and the control of global and localised plasma events, like Edge-Localised-Mode and disruptions. In this paper, we present an operational implementation of a new, generalised formulation of Bezier finite-elements applied to the JOREK code, a significant advancement from the previously G1-continuous bi-cubic Bezier elements. This new mathematical method enables any polynomial order of Bezier elements, with a guarantee of G-continuity at the level of (n−1)/2, for any odd n, where n is the order of the Bezier polynomials. The generalised method is defined, and a rigorous mathematical proof is provided for the G-continuity requirement. Key details on the code implementation are mentioned, together with a suite of tests to demonstrate the mathematical reliability of the finite-element method, as well as the practical usability for typical non-linear tokamak MHD simulations. A demonstration for a state-of-the-art simulation of an Edge-Localised-Mode instability in the future ITER tokamak, with realistic grid geometry, finalises the study.

This paper proposes a new Monte Carlo sensitivity analysis method for fixed source radiation transport problems, which is dubbed the derivative source method (DSM). This method is a variation of the formerly proposed perturbation source method. A transport equation of a derivative particle representing a derivative of a flux with respect to a parameter such as a cross section is derived by differentiating the fixed source radiation transport equation. This paper presents a Monte Carlo algorithm to solve this transport equation. The derivative particle is emitted from a region of interest (ROI) when a radiation particle undergoes a collision in the ROI. The derivative particle is tracked in the same manner as the ordinary radiation particles. The derivative particle that undergoes a collision in the ROI can yield another derivative particle whose derivative order is increased by one from the colliding particle. This higher-order derivative particle can be used for calculating the higher-order derivative of a flux. The differential operator sampling method (DOS), which is commonly used for Monte Carlo sensitivity analyses, suffers from poor performance when an ROI is small. For a small ROI, the efficiency of the DSM can be improved by adding a pseudo scattering cross section in the ROI, thereby increasing the pseudo scatterings and the number of derivative particles emitted from the ROI. The efficiency of the new method is evaluated by comparing the DSM to the DOS. Numerical tests are performed for a two-dimensional geometry containing a small inclusion. The results reveal that the DSM definitely outperforms the DOS for these test problems. The efficiency of the DSM depends strongly on the pseudo scattering cross section added to the inclusion.

The development of numerical solvers able to simulate compressible two-phase flows is still a great challenge in computational fluid dynamics. The interaction between acoustic waves and interfaces is of major concern for several engineering and biomedical applications, among which atomization in combustion chambers, cavitation problems, underwater explosions and bubble shock interactions. For instance, there are experimental evidences that acoustic waves can have an important effect on the atomization process, and this could have a great impact on combustion. However, usual approaches for DNS of primary atomization are based on incompressible solvers and therefore are not able to capture the propagation of acoustic waves and therefore cannot be used to simulate such phenomena. The numerical problem associated with the simulation of compressible two- phase flows is challenging, mostly because of the huge spatial variations of the speed of sound and the corresponding low Mach number in the liquid phase. In the present work, a numerical solver able to study subsonic compressible two-phase flows is presented. The solver is based on a complete formulation of the Navier-Stokes equations with real fluid equations of state, which are solved with a semi-implicit projection method. It is shown that the solver can handle a large range of compressible subsonic flows, both for a single phase or for two phases, as the flow induced by free convection, a bubble expansion in isothermal or isentropic conditions, and interaction between acoustic waves and liquid-gas interfaces. Eventually, attention will be given to the simulation of a water droplet in air, under the excitation of a stationary acoustic wave. It is also shown that the solver exhibits equivalent performances as an incompressible solver in configurations where compressible effects have no effects.

We develop a model which couples the flow in a discrete fracture to a deformable porous medium. To account for the discrete representation of the fracture, a dimensionally-reduced fluid flow model is proposed. The fluid flow model incorporates both a reduced permeability of the fracture walls due to the skin effect, and a slip of fluid flowing along the permeable fracture walls. Biot's model for poroelastic media is coupled to a fracture flow model based on a thin-film approximation of the compressible Navier-Stokes equations. The fracture flow model incorporates a fluid entry resistance parameter to relate the leak-off through the fracture walls to a pressure jump across the fracture walls, and the Beavers-Joseph-Saffman slip rate coefficient to represent the fluid slip along the fracture walls. The numerical model is based on a thermodynamic framework in which all energy storage and dissipative mechanisms in the problem are identified, including the mechanisms related to the interface effects. The thermodynamic framework is employed to solve the nonlinear coupled problem up to a specified energy range through a Picard iteration technique and to study the model and its results. Studies are presented for a range of fluid entry resistance parameters and Beavers-Joseph-Saffman slip rate coefficients, showing the capability of the model to simulate skin and slip effects in a dimensionally-reduced fracture setting.

A new explicit numerical scheme for integrating the relativistic equations of motion for electrically charged particles is proposed as an alternative to the Boris integrator. It has been known that the original Boris integrator includes a large numerical error in the relativistic motion, although the integrator has been used in particle-in-cell simulations of plasma for a half century. The present integrator approximates the theoretical trajectory of the relativistic E-cross-B motion for a charged particle more accurately than the previous explicit integrators such as the Boris, Vay, and Higuera-Cary ones.

This paper presents a topology optimization method in rarefied gas flow problems to obtain the optimal structure of a flow channel as a configuration of gas and solid domains. In this paper, the kinetic equation, the governing equation of rarefied gas flows, is extended over the entire design domain including solid domains assuming the solid as an imaginary gas for implicitly handling the gas-solid interfaces in the optimization process. Based on the extended equation, a 2D flow channel design problem is formulated, and the design sensitivity is obtained based on the Lagrange multiplier method and adjoint variable method. Both the rarefied gas flow and the adjoint flow are computed by a deterministic method based on a finite discretization of the molecular velocity space, rather than the DSMC method. The validity and effectiveness of our proposed method are confirmed through several numerical examples.

We proposed a novel multi-moment finite volume method (MMFVM) to compute compressible viscous flows on arbitrary unstructured grids. Unlike the previous volume-average/point-value multi-moment (VPM) method (Xie et al. 2014 [60] ), the present method, so-called VPM-Ex (VPM with extended-stencil reconstruction), formulates novel spatial reconstructions with substantially improved robustness and accuracy for both smooth and discontinuous solutions. Our efforts in this work have brought at least the following new features to the numerical formulation: 1) a more robust and accurate spatial reconstruction based on the stencil of all immediately adjacent cells that supports higher-order limiting projection; 2) two different options for both explicit and implicit reconstructions; 3) a simplified and more accurate formulation for point-value. In addition, we have proposed a smoothness-adaptive fitting (SAF) method for limiting projection to improve the solution quality for discontinuities. The resulting reconstruction method that combines VPM-Ex scheme with SAF-based limiting projection schemes is able to attain 3rd-order accuracy for smooth solution, and non-oscillatory and less-dissipative numerical results for discontinuous solution on unstructured grids of different types of elements. The numerical method has been extensively verified by various benchmark tests for scalar conservation equation, Euler equations and Navier–Stokes equations in 2 and 3 dimensions. The numerical results substantiate that the present method provides a novel numerical formulation of great practical significance to accurately resolve both continuous and discontinuous solutions.

A weakly compressible scheme using the interface-adapted adaptive mesh refinement (AMR) method is proposed for simulating low Mach number gas-liquid two-phase flows in large-scale and high-resolution simulations. A pressure evolution equation is derived from the iso-thermal process and low-Mach-number assumptions. We solve the Navier-Stokes equation and the pressure equation explicitly including acoustic waves. In the conventional semi-implicit method to solve incompressible two-phase flows, the computational cost of the linear solver increases as the problem size becomes larger. The conservative phase-field equation was solved using the finite volume method (FVM) to capture the gas-liquid interface while conserving the total mass of each phase. We developed GPU code for a tree-based AMR that greatly reduces the computational cost of assigning a high-resolution mesh around the moving interface region. The data structure of the memory pool has extra space allocated to prevent frequent memory allocations and deallocations. Results for the two-phase flow benchmark problems, 2D rising-bubble and dam-breaking onto dry floor problem, are in good agreement with the results of incompressible solvers. The two-phase flow simulation of the dam-breaking onto a wet floor problem maintained the shape interface regardless of whether the AMR method was used or not. We have computed a two-dimensional soap bubble growing from 16 mm to 120 mm in diameter with about 0.9 million total cells. The final thickness of the liquid film was about 0.1 mm with the finest cell size being 0.0195 mm , equivalent to 8 , 192 × 8 , 192 uniform cells. This computation showed that high-resolution two-phase flow simulation with the explicit scheme and AMR method reproduced the behavior of the thin liquid film.

International audience; Corona discharge modeling mostly relies on two, mostly distinct, approaches: high-fidelity, numerically challenging, unsteady simulations having high-computational cost or low-fidelity simulations based on empirical assumptions such as constant electric field at the emitter electrode. For the purpose of steady discharge current predictions, high-fidelity models are very costly to use whilst empirical models have limited range of validity owing the subtle use of tuned parameters. We propose an intermediate approach: an asymptotic multi-scale/two-domain numerical modeling based upon generalizing previous asymptotic axi-symmetrical analysis [1,2]. We show how the initial elliptic (electric potential), hyperbolic (charge transport), non-local (photo-ionization) problem can be formulated into two local problems coupled by matching conditions. The approach relies on a multipole expansion of the radiative photo-ionization source term (in two dimensions for cylindrical emitters). The analytical asymptotic matching conditions derived in [2]result in flux continuity conditions at the boundary of the two domains. These coupling conditions are enforced by Lagrange multipliers, within a variational formulation, leading to a hierarchy of non-linear coupled problems. The proposed approach is both monolithic and two-domains: two asymptotic regions, an inner-one associated with corona discharge, and an outer-one, the ion drift region. Numerical convergence and validations of the finite element implementation is provided. A comparison with various experimental results convincingly demonstrate the applicability of the method, which avoids tuning parameters dedicated to each specific configuration, but, on the contrary, exclusively relies on known and measurable physical quantities (e.g.,ion mobilities, photo-ionization coefficient, ionization electric field, Townsend discharge coefficient, etc...).

形態: カラー図版あり, Physical characteristics: Original contains color illustrations, 資料番号: PA2220001000

We propose an adaptive multiscale method to improve the efficiency and the accuracy of numerical computations by combining numerical homogenization and domain decomposition for modeling flow and transport. Our approach focuses on minimizing the use of fine scale properties associated with advection and diffusion/dispersion. Here a fine scale flow and transport problem is solved in subdomains defined by a transient region where spatial changes in transported species concentrations are large while a coarse scale problem is solved in the remaining subdomains. Away from the transient region, effective macroscopic properties are obtained using local numerical homogenization. An Enhanced Velocity Mixed Finite Element Method (EVMFEM) as a domain decomposition scheme is used to couple these coarse and fine subdomains [1] . Specifically, homogenization is employed here only when coarse and fine scale problems can be decoupled to extract temporal invariants in the form of effective parameters. In this paper, a number of numerical tests are presented for demonstrating the capabilities of this adaptive numerical homogenization approach in upscaling flow and transport in heterogeneous porous medium.

This paper considers an accurate and efficient numerical scheme for solving the radiative transfer equation (RTE) based on the discrete ordinates method (DOM) in highly forward-peaked scattering media. The DOM approximates the scattering integral of the RTE including the phase function into a quadrature sum with the total number of discrete angular directions (TND) by a quadrature set. Due to large numerical errors of the scattering integral based on the DOM in highly forward-peaked scattering, the phase function is renormalized to satisfy its normalization conditions. Although the renormalization approaches of the phase function improve the accuracy of the numerical results of the RTE, the computational efficiency of the RTE is still required. This paper develops the first order renormalization approach using the double exponential formula for three quadrature sets: level symmetric even, even and odd, and Lebedev sets in a wide range of the TND from 48 to 1454. Numerical errors of the three-dimensional time-dependent RTE are investigated by the analytical solutions of the RTE. The investigation shows that the level symmetric even set with the TND of 48 using the developed approach provides the most accurate results of the RTE among the quadrature sets in the range of the TND, while to obtain the same accuracy by the conventional zeroth order renormalization approach, the TND needs to be larger than 360. The results suggest the large reduction of computational loads by the developed approach to less than 10 percent from those in the conventional approach.

Numerical methods for solving the flow around a moving or deforming membrane are developed by employing the ideas of the direct-discretisation of the Navier–Stokes equation even in the immediate vicinity of the object surface and consistent-discretisation of the pressure Poisson equation with the incompressible velocity field (i.e., consistent-coupling) that incorporates the boundary conditions on the surface to the pressure equation. Comparative study of three different discretisation strategies is carried out to highlight the effect of the consistent and direct discretisations. The validity of the present “consistent direct discretisation” is established through comparisons with the analytical solutions for some fundamental shear-driven 2-D flow fields with a moving membrane of flat and corrugated geometries. Also, the flows induced by a membrane of circular geometry (i.e., particle) are compared with the reference numerical results under prescribed motion in a stationary fluid as well as lateral migration in a shear flow. A three dimensional problem is presented for an interaction problem between a spherical particle and Taylor–Green vortices, and the result is verified by comparing with the independently-conducted numerical results. Finally, the method is applied to an interaction problem between the fluid and flexible filament showing strong flapping and snapping motions.

形態: カラー図版あり, Physical characteristics: Original contains color illustrations, Accepted: 2018-09-30, 資料番号: PA1910002000

We extend the recently introduced divergence-conforming immersed boundary (DCIB) method [1] to fluid-structure interaction (FSI) problems involving closed co-dimension one solids. We focus on capsules and vesicles, whose discretization is particularly challenging due to the higher-order derivatives that appear in their formulations. In two-dimensional settings, we employ cubic B-splines with periodic knot vectors to obtain discretizations of closed curves with C^2 inter-element continuity. In three-dimensional settings, we use analysis-suitable bi-cubic T-splines to obtain discretizations of closed surfaces with at least C^1 inter-element continuity. Large spurious changes of the fluid volume inside closed co-dimension one solids is a well-known issue for IB methods. The DCIB method results in volume changes orders of magnitude lower than conventional IB methods. This is a byproduct of discretizing the velocity-pressure pair with divergence-conforming B-splines, which lead to negligible incompressibility errors at the Eulerian level. The higher inter-element continuity of divergence-conforming B-splines is also crucial to avoid the quadrature/interpolation errors of IB methods becoming the dominant discretization error. Benchmark and application problems of vesicle and capsule dynamics are solved, including mesh-independence studies and comparisons with other numerical methods., For supplementary movies go to https://www.andrew.cmu.edu/user/hugocp/research.html

Subsurface geological formations provide giant capacities for large-scale (TWh) storage of renewable energy, once this energy (e.g. from solar and wind power plants) is converted to green gases, e.g. hydrogen. The critical aspects of developing this technology to full-scale will involve estimation of storage capacity, safety, and efficiency of a subsurface formation. Geological formations are often highly heterogeneous and, when utilized for cyclic energy storage, entail complex nonlinear rock deformation physics. In this work, we present a novel computational framework to study rock deformation under cyclic loading, in presence of nonlinear time-dependent creep physics. Both classical and relaxation creep methodologies are employed to analyze the variation of the total strain in the specimen over time. Implicit time-integration scheme is employed to preserve numerical stability, due to the nonlinear process. Once the computational framework is consistently defined using finite element method on the fine scale, a multiscale strategy is developed to represent the nonlinear deformation not only at fine but also coarser scales. This is achieved by developing locally computed finite element basis functions at coarse scale. The developed multiscale method also allows for iterative error reduction to any desired level, after being paired with a fine-scale smoother. Numerical test cases are studied to investigate various aspects of the developed computational workflow, from benchmarking with experiments to analysing the impact of nonlinear deformation for a field-scale relevant environment. Results indicate the applicability of the developed multiscale method in order to employ nonlinear physics in their laboratory-based scale of relevance (i.e., fine scale), yet perform field-relevant simulations. The developed simulator is made publicly available at https://gitlab.tudelft.nl/ADMIRE_Public/mechanics .

A general linearisation procedure for the consistent tangent of a small-strain visco-plastic material model is presented in this note. The procedure is based on multi-variable linearisation around a so-called 'reference state'. In particular, the linerarisation of the time integration scheme is found to yield an extra term compared to classical expressions, which only appears because the material response is time-dependent. It has the effect of yielding a very accurate initial guess for the Newton-Raphson protocol based on the ongoing viscous flow. It is shown, using a modern variational FFT-based solver, that the extra term reduces both the CPU time and the number of Newton-Raphson iterations by around a factor two., Comment: Journal of Computational Physics, 2020

This paper introduces three new Schur complement approximations for the augmented Lagrangian preconditioner. The incompressible Navier-Stokes equations discretized by a stabilized finite element method are utilized to evaluate these new approximations of the Schur complement. A wide range of numerical experiments in the laminar context determines the most efficient Schur complement approximation and investigates the effect of the Reynolds number, mesh anisotropy and refinement on the optimal choice. Furthermore, the advantage over the traditional Schur complement approximation is exhibited.

We present a method for the design of a single freeform reflector that converts the light distribution of a point source to a desired light distribution in the far field. Using the geometrical-optics law of reflection and requiring energy conservation, this optical design problem can be represented by a generalized Monge–Ampere equation for the shape of the reflector with transport boundary condition. We use a generalized least-squares algorithm that can handle a logarithmic cost function in the corresponding optimal transport problem. The algorithm first computes the optical map and subsequently constructs the optical surface. We demonstrate that the algorithm can generate reflector surfaces for a number of complicated target distributions.

International audience; A fully Eulerian approach to predict fluids-membrane behaviours is presented in this paper. Based on the numerical model proposed by Ii et al. (2012), we present a sharp methodology to account for the jump conditions due to hyperelastic membranes. The membrane is considered infinitely thin and is represented by the level set method. Its deformations are obtained from the transport of the components of the left Cauchy-Green tensor throughout time. Considering the linear or a hyperelastic material law, the surface stress tensor is computed and gives the force exerted by the membrane on the surrounding fluids. The membrane force is taken into account in the Navier-Stokes equations as jump conditions on the pressure and on the velocity derivatives by imposing suitable singular source terms in cells crossed by the interface. To prevent stability issues, an extension algorithm has been developed to remove the normal derivatives of the scalar fields specific to the membrane. In particular, a subcell resolution at the interface of the extrapolated variable is proposed for increasing the accuracy of the extension algorithm. These improvements are validated by comparing our numerical results with benchmarks from the literature. Moreover, a new benchmark is proposed for fluids with both different viscosities and different densities to target applications where a gas and a liquid phase are separated by a membrane.

A low-dissipation simulation method is used to perform simulations of transitional aerodynamic flow over a delta wing. For an accurate simulation of such a flow, numerical conservation of important physical quantities is desirable. In particular, the discretization of the convective terms of the Navier-Stokes equations should not spuriously generate or dissipate kinetic energy, because this can interfere with the transition to turbulent flow. Conservation of discrete kinetic energy by the discretized convective terms can be achieved by writing the Navier--Stokes equations in square-root variables, which results in a skew-symmetric convective term. In the paper, simulations with such a low-dissipation method are presented at chord Reynolds numbers around 200,000. The results show good agreement with experimental measurements.

Controlling large particle systems in collective dynamics by a few agents is a subject of high practical importance, e.g., in evacuation dynamics. In this paper we study an instantaneous control approach to steer an interacting particle system into a certain spatial region by repulsive forces from a few external agents, which might be interpreted as shepherd dogs leading sheep to their home. We introduce an appropriate mathematical model and the corresponding optimization problem. In particular, we are interested in the interaction of numerous particles, which can be approximated by a mean-field equation. Due to the high-dimensional phase space this will require a tailored optimization strategy. The arising control problems are solved using adjoint information to compute the descent directions. Numerical results on the microscopic and the macroscopic level indicate the convergence of optimal controls and optimal states in the mean-field limit,i.e., for an increasing number of particles., Comment: arXiv admin note: substantial text overlap with arXiv:1610.01325

In this article we solve the inverse reflector problem for a light source emitting a parallel light bundle and a target in the far-field of the reflector by use of a least-squares method. We derive the Monge–Ampère equation, expressing conservation of energy, while assuming an arbitrary coordinate system. We generalize a Cartesian coordinate least-squares method presented earlier by Prins et al. [13] to arbitrary orthogonal coordinate systems. This generalized least-squares method provides us the freedom to choose a coordinate system suitable for the shape of the light source. This results in significantly increased numerical accuracy. Decrease of errors by factors up to 104 is reported. We present the generalized least-squares method and compare its numerical results with the Cartesian version for a disk-shaped light source.

In this paper, we extend the implicit-explicit (IMEX) methods of Peer type recently developed in [Lang, Hundsdorfer, J. Comp. Phys., 337:203--215, 2017] to a broader class of two-step methods that allow the construction of super-convergent IMEX-Peer methods with A-stable implicit part. IMEX schemes combine the necessary stability of implicit and low computational costs of explicit methods to efficiently solve systems of ordinary differential equations with both stiff and non-stiff parts included in the source term. To construct super-convergent IMEX-Peer methods with favourable stability properties, we derive necessary and sufficient conditions on the coefficient matrices and apply an extrapolation approach based on already computed stage values. Optimised super-convergent IMEX-Peer methods of order s+1 for s=2,3,4 stages are given as result of a search algorithm carefully designed to balance the size of the stability regions and the extrapolation errors. Numerical experiments and a comparison to other IMEX-Peer methods are included., Comment: 22 pages, 4 figures. arXiv admin note: text overlap with arXiv:1610.00518

This study develops a new Lagrangian particle method for modeling flow and transport phenomena in complex porous media with discontinuities. For instance, diffusion processes can be modeled by Lagrangian Random Walk algorithms. However, discontinuities and heterogeneities are difficult to treat, particularly discontinuous diffusion D ( x ) or porosity θ ( x ) . In the literature on particle Random Walks, previous methods used to handle this discontinuity problem can be characterized into two main classes as follows: “Interpolation techniques”, and “Partial reflection methods”. One of the main drawbacks of these methods is the small time step required in order to converge to the expected solution, particularly in the presence of many interfaces. These restrictions on the time step, lead to inefficient algorithms. The Random Walk Particle Tracking (RWPT) algorithm proposed here is, like others in the literature, discrete in time and continuous in space (gridless). We propose a novel approach to partial reflection schemes without restrictions on time step size. The new RWPT algorithm is based on an adaptive “Stop&Go” time-stepping, combined with partial reflection/refraction schemes, and extended with a new concept of negative mass particles. To test the new RWPT scheme, we develop analytical and semi-analytical solutions for diffusion in the presence of multiple interfaces (discontinuous multi-layered medium). The results show that the proposed Stop&Go RWPT scheme (with adaptive negative mass particles) fits extremely well the semi-analytical solutions, even for very high contrasts and in the neighborhood of interfaces. The scheme provides a correct diffusive solution in only a few macro-time steps, with a precision that does not depend on their size.

In this paper, a fast linearized conservative finite element method is studied for solving the strongly coupled nonlinear fractional Schrodinger equations. We prove that the scheme preserves both the mass and energy, which are defined by virtue of some recursion relationships. Using the Sobolev inequalities and then employing the mathematical induction, the discrete scheme is proved to be unconditionally convergent in the sense of L 2 -norm and H α / 2 -norm, which means that there are no any constraints on the grid ratios. Then, the prior bound of the discrete solution in L 2 -norm and L ∞ -norm are also obtained. Moreover, we propose an iterative algorithm, by which the coefficient matrix is independent of the time level, and thus it leads to Toeplitz-like linear systems that can be efficiently solved by Krylov subspace solvers with circulant preconditioners. This method can reduce the memory requirement of the proposed linearized finite element scheme from O ( M 2 ) to O ( M ) and the computational complexity from O ( M 3 ) to O ( M log ⁡ M ) in each iterative step, where M is the number of grid nodes. Finally, numerical results are carried out to verify the correction of the theoretical analysis, simulate the collision of two solitary waves, and show the utility of the fast numerical solution techniques.

Accepted: 2017-10-05, 資料番号: SA1170187000

In this paper, we propose a simple and accurate numerical method for capturing moving interfaces on fixed Eulerian grids by coupling the Tangent of Hyperbola Interface Capturing (THINC) method and Level Set (LS) method. The innovative and practically-significant aspects of the proposed method, so-called THINC/LS method, lie in (1) representing the interface with polynomial of high-order (arbitrary order in principle) rather than the plane representation commonly used in the Piecewise Linear Interface Calculation (PLIC) Volume of fluid (VOF) methods, (2) conserving rigorously the mass of the transported VOF field, (3) being able to resolving fine interface structures under mesh resolution, and (4) providing a straightforward and easy-to-code algorithm for 3D implementation. We verified the proposed scheme with the widely used benchmark tests. Numerical results show that this new method can obtain high-order accuracy for interface reconstruction and can produce more accurate results in capturing moving interfaces compared to the classical VOF methods.

A novel time integration method of the drift kinetic equation is proposed, where low order fluid moment equations including the lowest order terms for the dispersive Alfven wave propagation are extracted from the electron drift kinetic equations. The moment extract method enables ones to implement an implicit solver for wave propagation by means of the operator splitting, while the kinetic part is solved explicitly. Numerical tests of the new scheme have verified stable and accurate time-integration of the drift kinetic equation and enabled to take a large time step size when the electron β value is smaller than the electron-to-ion mass ratio.

This paper presents improvement and performance evaluation of the “perturbation source method”, which is one of the Monte Carlo perturbation techniques. The formerly proposed perturbation source method was first-order accurate, although it is known that the method can be easily extended to an exact perturbation method. A transport equation for calculating an exact flux difference caused by a perturbation is solved. A perturbation particle representing a flux difference is explicitly transported in the perturbed system, instead of in the unperturbed system. The source term of the transport equation is defined by the unperturbed flux and the cross section (or optical parameter) changes. The unperturbed flux is provided by an “on-the-fly” technique during the course of the ordinary fixed source calculation for the unperturbed system. A set of perturbation particle is started at the collision point in the perturbed region and tracked until death. For a perturbation in a smaller portion of the whole domain, the efficiency of the perturbation source method can be improved by using a virtual scattering coefficient or cross section in the perturbed region, forcing collisions. Performance is evaluated by comparing the proposed method to other Monte Carlo perturbation methods. Numerical tests performed for a particle transport in a two-dimensional geometry reveal that the perturbation source method is less effective than the correlated sampling method for a perturbation in a larger portion of the whole domain. However, for a perturbation in a smaller portion, the perturbation source method outperforms the correlated sampling method. The efficiency depends strongly on the adjustment of the new virtual scattering coefficient or cross section.

The original Roe scheme is well-known to be unsuitable in simulations of turbulence because the dissipation that develops is unsatisfactory. Simulations of turbulent channel flow for Re τ = 180 show that, with the ‘low-Mach-fix for Roe’ (LMRoe) proposed by Rieper [J. Comput. Phys. 230 (2011) 5263–5287], the Roe dissipation term potentially equates the simulation to an implicit large eddy simulation (ILES) at low Mach number. Thus inspired, a new implicit turbulence model for low Mach numbers is proposed that controls the Roe dissipation term appropriately. Referred to as the automatic dissipation adjustment (ADA) model, the method of solution follows procedures developed previously for the truncated Navier–Stokes (TNS) equations and, without tuning of parameters, uses the energy ratio as a criterion to automatically adjust the upwind dissipation. Turbulent channel flow at two different Reynold numbers and the Taylor–Green vortex were performed to validate the ADA model. In simulations of turbulent channel flow for Re τ = 180 at Mach number of 0.05 using the ADA model, the mean velocity and turbulence intensities are in excellent agreement with DNS results. With Re τ = 950 at Mach number of 0.1, the result is also consistent with DNS results, indicating that the ADA model is also reliable at higher Reynolds numbers. In simulations of the Taylor–Green vortex at Re = 3000 , the kinetic energy is consistent with the power law of decaying turbulence with −1.2 exponents for both LMRoe with and without the ADA model. However, with the ADA model, the dissipation rate can be significantly improved near the dissipation peak region and the peak duration can be also more accurately captured. With a firm basis in TNS theory, applicability at higher Reynolds number, and ease in implementation as no extra terms are needed, the ADA model offers to become a promising tool for turbulence modeling.

We solve the 2D transverse-electrically polarized domain-integral equation in a layered background medium by applying a Gabor frame as a projection method. This algorithm employs both a spatial and a spectral discretization of the electric field and the contrast current in the direction of the layer extent. In the spectral domain we use a representation on the complex plane that avoids the poles and branchcuts found in the Green function. Because of the special choice of the complex-plane path in the spectral domain and because of the choice to use a Gabor frame to represent functions on this path, fast algorithms based on FFTs are available to transform to and from the spectral domain, yielding an O ( N log ⁡ N ) scaling in computation time.

Accepted: 2017-02-23, 資料番号: SA1170049000

The evaporation of sessile multi-component droplets is modeled with an axisymmetic finite element method. The model comprises the coupled processes of mixture evaporation, multi-component flow with composition-dependent fluid properties and thermal effects. Based on representative examples of water–glycerol and water–ethanol droplets, regular and chaotic examples of solutal Marangoni flows are discussed. Furthermore, the relevance of the substrate thickness for the evaporative cooling of volatile binary mixture droplets is pointed out. It is shown how the evaporation of the more volatile component can drastically decrease the interface temperature, so that ambient vapor of the less volatile component condenses on the droplet. Finally, results of this model are compared with corresponding results of a lubrication theory model, showing that the application of lubrication theory can cause considerable errors even for moderate contact angles of 40°.

Quantitative phase-field models have been developed as feasible computational tools for solving the free-boundary problem in solidification processes. These models are constructed with some polynomials of the phase-field variable that describe variations of the physical quantities inside the diffuse interface. The accuracy of the simulation depends on the choice of the polynomials and such dependence is indispensable for high-performance computing and valuable for extending the range of applications of the model to several physical systems. However, little is known about the dependence of the accuracy on the choice of the polynomials. In this study, numerical testing is carried out for quantitative phase-field models with extensive sets of polynomials (24 different models) for isothermal solidification in binary alloys. It is demonstrated in two-dimensional simulations of dendritic growth that a specific set of polynomials must be employed to achieve high accuracy in the models with double-well and double-obstacle potentials. Both types of model with the best set of polynomials yield almost the same numerical accuracy. (C) 2017 Elsevier Inc. All rights reserved.

形態: カラー図版あり, Physical characteristics: Original contains color illustrations, Accepted: 2017-04-01, 資料番号: PA1820013000

Since the beginning of the industrial age, material performance and design have been in the midst of innovation of many disruptive technologies. Today’s electronics, space, medical, transportation, and other industries are enriched by development, design and deployment of composite, heterogeneous and multifunctional materials. As a result, materials innovation is now considerably outpaced by other aspects from component design to product cycle. In this article, we review predictive nonlinear theories for multiscale modeling of heterogeneous materials. Deeper attention is given to multiscale modeling in space and to computational homogenization in addressing challenging materials science questions. Moreover, we discuss a state-of-the-art platform in predictive image-based, multiscale modeling with co-designed simulations and experiments that executes on the world’s largest supercomputers. Such a modeling framework consists of experimental tools, computational methods, and digital data strategies. Once fully completed, this collaborative and interdisciplinary framework can be the basis of Virtual Materials Testing standards and aids in the development of new material formulations. Moreover, it will decrease the time to market of innovative products.

In this work we present a mimetic spectral element discretization for the 2D incompressible Navier–Stokes equations that in the limit of vanishing dissipation exactly preserves mass, kinetic energy, enstrophy and total vorticity on unstructured triangular grids. The essential ingredients to achieve this are: (i) a velocity–vorticity formulation in rotational form, (ii) a sequence of function spaces capable of exactly satisfying the divergence free nature of the velocity field, and (iii) a conserving time integrator. Proofs for the exact discrete conservation properties are presented together with numerical test cases on highly irregular triangular grids.

We propose a novel Mach-uniform numerical model for 2D Euler equations on unstructured grids by using multi-moment finite volume method. The model integrates two key components newly developed to solve compressible flows on unstructured grids with improved accuracy and robustness. A new variant of AUSM scheme, so-called AUSM+-pcp (AUSM+ with pressure-correction projection), has been devised including a pressure-correction projection to the AUSM+ flux splitting, which maintains the exact numerical conservativeness and works well for all Mach numbers. A novel 3th-order, non-oscillatory and less-dissipative reconstruction has been proposed by introducing a multi-dimensional limiting and a BVD (boundary variation diminishing) treatment to the VPM (volume integrated average (VIA) and point value (PV) based multi-moment) reconstruction. The resulting reconstruction scheme, the limited VPM-BVD formulation, is able to resolve both smooth and non-smooth solutions with high fidelity. Benchmark tests have been used to verify the present model. The numerical results substantiate the present model as an accurate and robust unstructured-grid formulation for flows of all Mach numbers.

A new numerical method for the solution of an internally mixed spatially homogeneous sectional model for aerosol nucleation and condensation is proposed. The characteristics method is used to predict droplet sizes within a discrete time step. The method is de- signed such that 1) a pre-specified number of moments of the droplet size distribution may be preserved, 2) there exists no time step stability restriction related to the condensa- tion rate and section size, 3) highly skewed fixed sectional distributions may be used and 4) it is straightforward to extend to spatially inhomogeneous settings and to incorporate droplet coagulation and break-up. We derive, starting from mass conservation, a consis- tent internally mixed multi-species aerosol model. For certain condensational growth laws analytical solutions exist, against which the method is validated. Using two-moment and four-moment-preserving schemes, we find first order convergence of the numerical solu- tion to the analytical result, as a function of the number of sections. As the four-moment- preserving scheme does not guarantee positivity of the solution, a hybrid scheme is pro- posed, which, when needed, locally reverts back to two-moment preservation, to prevent negativity. As an illustration, the method is applied to a complete multi-species homoge- neous nucleation and condensation problem.

We proposed a multi-moment constrained finite volume method which can simulate incompressible flows of high Reynolds number in complex geometries. Following the underlying idea of the volume-average/point-value multi-moment (VPM) method (Xie et al. (2014) [71]), this formulation is developed on arbitrary unstructured hybrid grids by employing the point values (PV) at both cell vertex and barycenter as the prognostic variables. The cell center value is updated via an evolution equation derived from a constraint condition of finite volume form, which ensures the rigorous numerical conservativeness. Novel numerical formulations based on the local PVs over compact stencil are proposed to enhance the accuracy, robustness and efficiency of computations on unstructured meshes of hybrid and arbitrary elements. Numerical experiments demonstrate that the present numerical model has nearly 3-order convergence rate with numerical errors much smaller than the VPM method. The numerical dissipation has been significantly suppressed, which facilitates numerical simulations of high Reynolds number flows in complex geometries.

International audience; We consider the implementation of a friction contact angle model in a Navier-Stokes VoF-CSF solver for the simulation of moving contact lines at the nano-scale. A liquid-liquid interface confined in a Couette flow generated by two solid walls moving at the same velocity in opposite directions is considered to discuss the relevance of the friction model. The simulations are compared with a reference case obtained using MD simulations by Qian et al. [46]. We show that the Navier Stokes simulations are able to reproduce the MD simulations for both the interface shape and the velocity field. The appropriate contact line friction is found to be grid convergent and of the same order as the friction measured in MD simulations. A detailed investigation of the interface shape has revealed an auto-similar linear profile in the center of the channel. Close to the wall the interface shape follows the classical Log evolution given by the Cox relation despite the wall confinement.