A front tracking method is proposed to deal with compressible flows involving sharp interfaces. It relies on a first-order finite-volumes scheme of Lagrange-Projection type. While the Lagrangian step of the method is classical, the projection step is based on a pseudo-random sampling technique in the spirit of the one used in the Glimm’s scheme. The scheme allows reducing the numerical diffusion at the interface, in the sense that they remain sharp. It has robustness and convergence properties that are not present in most of the schemes proposed previously, and it can be applied to unstructured meshes. While this new method works very well on structured meshes, improvements are still needed in order to achieve accurate results on unstructured meshes (triangles).

For safety studies of nuclear reactor cores, a finite-volume thermal-hydraulic code with a porous medium approach named THYC-coeur has been developed by EDF to simulate steady-state flows of a two-phase mixture within the core of a nuclear reactor. The steady-state solution is obtained through a fictitious transient. Despite a relatively low individual computational time, many state points are considered in the safety studies, which can represent significant CPU time. To speed up the computation, one possible objective is to reduce the number of iterations (i.e. the number of time steps) required to reach convergence. In the present work, the idea is to train a neural network (NN) to predict steady-state solutions and use this prediction to initialize the transient computation. This method allows combinating the advantages of NN prediction, in terms of rapidity, with that of the THYC-coeur model, in terms of the physical validation of the solution. To evaluate the potential of this method, a simplified one-dimensional code was designed. This code simulates a two-phase water vapor flow in a heated channel. A NN was trained to predict the solution fields from imposed boundary conditions. In this paper, we present the methodology, the database selection process, the structure of the NN, and the optimization of the network’s hyperparameters. This paper examines two different physical models: the 3-equation model and the 4-equation model. Initially, a simple loss function is used to predict the fields of these two models. The observed accelerations are approximately 70% for the 3-equation model and 48% for the 4-equation model. A detailed study of the correlation between prediction accuracy and the resulting acceleration has shown that the low-frequency components in the entropy field prediction error significantly slow down the search for the steady state. The highlight of this work is that by introducing spatial frequencies in the error for the optimization of the NN, the number of iterations is reduced between 61% (4-equation model) and 83% (3-equation model) from baseline simulations.

This work presents a simplified model of compressible multiphase fluid flow in a heated porous medium. We first introduce the model and its numerical approximation using a linearized implicit finite volume scheme. We then propose a technique to accelerate the implicit scheme through a machine learning approach.

This paper is dedicated to Richtmyer-Meshkov simulations. The strategy adopted here is not classical. It is based on a two-fluid Euler model, whose approximated solutions are computed using a first-order scheme coupled with a pseudo-random front-tracking algorithm. This new method has been tested satisfactorily, demonstrating good accuracy, with an effective convergence rate close to 0.9 even on linearly degenerate fields. This first application to the Richtmyer-Meshkov instability shows satisfactory agreement with experiments and exhibits appreciable properties: no spurious velocity/pressure oscillations show up near the interface, and the interface is maintained sharp.

We present a novel framework for the development of fourth-order lattice Boltzmann schemes to tackle multidimensional nonlinear systems of conservation laws. As for other numerical schemes for hyperbolic problems, high-order accuracy applies only to smooth solutions. Our numerical schemes preserve two fundamental characteristics inherent in classical lattice Boltzmann methods: a local relaxation phase and a transport phase composed of elementary shifts on a Cartesian grid. Achieving fourth-order accuracy is accomplished through the composition of second-order time-symmetric basic schemes utilizing rational weights. This enables the representation of the transport phase in terms of elementary shifts. Introducing local variations in the relaxation parameter during each stage of relaxation ensures entropy stability of the schemes. This not only enhances stability in the long-time limit but also maintains fourth-order accuracy. To validate our approach, we conduct comprehensive testing on scalar equations and systems in both one and two spatial dimensions.

We propose a new parallel Discontinuous Galerkin method for the approximation of hyperbolic systems of conservation laws. The method remains stable with large time steps, while keeping the complexity of an explicit scheme: it does not require the assembly and resolution of large linear systems for the time iterations. The approach is based on a kinetic representation of the system of conservation laws previously investigated by the authors. In this paper, the approach is extended with a subdomain strategy that improves the parallel scaling of the method on computers with distributed memory.

Three Finite Volume schemes are proposed in this note to satisfy the maximum principle for the mass fraction y, solution of an unsteady balance equation, including a relative velocity between phases and a source term. The continuous maximum principle is examined first. Then, linear implicit discrete schemes are detailed in a multi-dimensional and unstructured framework.

We perform a stability analysis of the Vectorial Lattice-Boltzmann Method (VLBM). The VLBM has been introduced in [1–3, 9, 18]. It is a variant of the LBM with extended stability features: it allows handling compressible flows with shock waves, while the LBM is limited to low-Mach number regime. The stability analysis is based on the Legendre transform theory. We also propose a new tool: the equivalent system analysis, which we conjecture to contains both the stability and the consistency of the VLBM.

High-performance computing in fluid dynamics frequently confronts substantial memory demands, especially in large-scale applications. Data compression techniques can alleviate these memory constraints, but introduce new challenges. This paper introduces an innovative on-the-fly low-overhead lossy compression technique tailored for GPU-based fluid simulations, utilizing the discrete wavelet transform (DWT). The technique is applicable to any numerical scheme where the data is stored on a regular grid and the time step is computed using a stencil. Our approach significantly diminishes memory requirements, achieving up to a 10-fold long-term reduction on a D3Q27 simulation, while minimally impacting the simulation accuracy. The methodology is built around careful design choices to achieve a satisfactory compression ratio/speed trade-off. It effectively maintains mass conservation and accurately preserves essential discontinuities in simulations. Extensive testing with a D3Q27 Lattice-Boltzmann method (LBM) simulation on a single GPU has shown that large-scale grids can be processed with minimal impact on the simulation accuracy and acceptable compression times. This compression technique demonstrates a robust capability to handle memory limitations in fluid simulations, opening the door to more complex and larger-scale simulations.

This paper presents a new solution to address the challenge of increasing memory usage in high-performance computing simulations on structured grids. Our approach utilizes a lossy compression scheme based on the Discrete Wavelet Transform (DWT) to achieve high compression ratios while preserving the accuracy of the simulation. Our evaluation on a finite volume scheme demonstrates that the approach can reduce memory usage by several orders of magnitude.

WeHélie, Romane introduceHelluy, Philippe a general framework for applying boundary conditions in the vectorial kinetic scheme of Bouchut [2, 4]. The method ensures entropy stability of the resulting approximation but also high order accuracy.

This paper presents a new solution to address the challenge of increasing memory usage in high-performance computing simulations of Lattice-Bolzmann or Finite-Volume schemes.Our approach utilises a lossy compression scheme based on the Discrete Wavelet Transform (DWT) to achieve high compression ratios while preserving the accuracy of the simulation.Our evaluation on two different FV/LBM schemes demonstrates that the approach can reduce memory usage by several orders of magnitude.

This paper is devoted to the simulation of compressible magnetohydrodynamic (MHD) flows with the Lattice Boltzmann Method (LBM). The usual LBM is limited to low-Mach flows. We propose a robust and accurate numerical method based on the vectorial kinetic construction of [5,25], which allows us to extend the LBM to arbitrary Mach flows. We also explain how to adjust the numerical viscosity in order to obtain stable and accurate results in smooth or discontinuous parts of the flow and reduced divergence errors. The method can handle shock waves and can be made second order in smooth regions. It is also very well adapted to computing with Graphics Processing Unit (GPU). Our GPU implementation in 2D achieves state-of-the-art accuracy, with near-optimal performance. We finally present numerical computations of a tilt instability that demonstrate the capability of the method to handle physically relevant simulations.

We propose a new stability analysis of the Vectorial Lattice-Boltzmann Method (VLBM). The VLBM is a variant of the LBM with extended stability features: it allows to handle compressible flows with shock waves, while the LBM is limited to low-Mach number regime. The stability analysis is based on the Legendre transform theory. We also propose a new tool: the equivalent system analysis, which we conjecture to contains both the stability and the consistency of the VLBM.

We present an efficient solver for the conservative transport equation with variable coefficients in complex toroidal geometries.The solver is based on a kinetic formulation resembling the Lattice-Boltzmann approach.The chosen formalism allows to obtain an explicit and conservative scheme that requires no matrix inversion and whose CFL stability condition is independent from the poloidal dynamics.We present the method and its optimized parallel implementation on toroidal geometries.Two and three dimensional plasma physics test cases are carried out.

We describe a parallel and quasi-explicit Discontinuous Galerkin (DG) kinetic scheme for solving systems of balance laws. The solver is unconditionally stable (i.e., the CFL number can be arbitrary) and has the complexity of an explicit scheme. It can be applied to any hyperbolic system of balance laws, see [2], [21]. In this work, we assess the performance of the scheme in the particular cases of the three-dimensional wave equation and of Maxwell's equations. We measure the benefit of the unconditional stability by performing experiments with very large CFL numbers. In addition, the parallel possibilities of the method are investigated.