English
Related papers

Related papers: Finite Volume approximations of the Euler system w…

200 papers

This paper presents a finite volume method for simulating two-phase flows using a level set approach coupled with volume of fluid method capable of simulating sharp fluid interfaces. The efficiency of the method is a result of the fact that…

Computational Physics · Physics 2022-07-20 Konstantinos G. Lyras , Jack Lee

Entropy stabilization of the compressible Euler system is achieved by adapting the averages that are applied to the density and internal energy variables. The approach achieves non-linear robustness despite the use of simplified symmetric…

Fluid Dynamics · Physics 2026-05-21 Carlo De Michele , Ayaboe K. Edoh

We consider a compressible Euler system with singular velocity alignment, known as the Euler-alignment system, describing the flocking behaviors of large animal groups. We establish a local well-posedness theory for the system, as well as a…

Analysis of PDEs · Mathematics 2020-07-17 Li Chen , Changhui Tan , Lining Tong

This study proposes a novel spatial discretization procedure for the compressible Euler equations which guarantees entropy conservation at a discrete level when an arbitrary equation of state is assumed. The proposed method, based on a…

Fluid Dynamics · Physics 2025-09-24 Alessandro Aiello , Carlo De Michele , Gennaro Coppola

We propose a finite volume scheme for a class of nonlinear parabolic equations endowed with non-homogeneous Dirichlet boundary conditions and which admit relative en-tropy functionals. For this kind of models including porous media…

Numerical Analysis · Mathematics 2017-04-21 Francis Filbet , Maxime Herda

The present paper introduces a class of finite volume schemes of increasing order of accuracy in space and time for hyperbolic systems that are in conservation form. This paper specifically focuses on Euler system that is used for modeling…

Computational Physics · Physics 2009-11-13 Dinshaw S. Balsara , Tobias Rumpf , Michael Dumbser , Claus-Dieter Munz

We consider the compressible Euler system with anelastic scaling, modeling isentropic flows under the influence of gravity. In the zero-Mach-number limit, the solution of the compressible Euler system converges to a variable density…

Numerical Analysis · Mathematics 2026-04-14 Marco Artiano , Hendrik Ranocha , Saurav Samantaray

We propose an upwind finite volume method for a system of two kinetic equations in one dimension that are coupled through nonlocal interaction terms. These cross-interaction systems were recently obtained as the mean-field limit of a…

Numerical Analysis · Mathematics 2023-09-15 Julia I. M. Hauser , Valeria Iorio , Markus Schmidtchen

We discuss numerical strategies to deal with PDE systems describing traffic flows, taking into account a density threshold, which restricts the vehicles density in the situation of congestion. These models are obtained through asymptotic…

Numerical Analysis · Mathematics 2016-12-13 Florent Berthelin , Thierry Goudon , Bastien Polizzi , Magali Ribot

This paper presents a novel structure-preserving scheme for Euler equations, focusing on the numerical conservation of entropy and kinetic energy. Explicit flux functions engineered to conserve entropy are introduced within the…

Numerical Analysis · Mathematics 2025-05-20 Kunal Bahuguna , Ramesh Kolluru , S. V. Raghurama Rao

The M1 moment model for electronic transport is commonly used to describe non-local thermal transport effects in laser-plasma simulations. In this article, we propose a new asymptotic-preserving scheme based on the Unified Gas Kinetic…

Numerical Analysis · Mathematics 2025-04-09 Jean-Luc Feugeas , Julien Mathiaud , Luc Mieussens , Thomas Vigier

In this paper we design, analyze and simulate a finite volume scheme for a cross-diffusion system which models chemotaxis with local sensing. This system has the same Lyapunov function (or entropy) as the celebrated minimal Keller-Segel…

Numerical Analysis · Mathematics 2025-10-07 Maxime Herda , Ariane Trescases , Antoine Zurek

We aim at providing a characterization of the ability to maintain a stochastic coupled system with porous media components in a prescribed set of constraints by using internal controls. This property is proven via a quasi-tangency…

Optimization and Control · Mathematics 2022-01-24 Ioana Ciotir , Dan Goreac , Ionut Munteanu

The kinetic theory provides a physical basis for developing multiscal methods for gas flows covering a wide range of flow regimes. A particular challenge for kinetic schemes is whether they can capture the correct hydrodynamic behaviors of…

Numerical Analysis · Mathematics 2025-08-12 Zhaoli Guo , Jiequan Li , Kun Xu

In this work we present a novel second order accurate well balanced Arbitrary-Lagrangian-Eulerian (ALE) finite volume scheme on moving nonconforming meshes for the Euler equations of compressible gasdynamics with gravity in cylindrical…

Numerical Analysis · Mathematics 2018-03-16 Elena Gaburro , Manuel J. Castro , Michael Dumbser

This paper is concerned with the approximation of the compressible Euler equations supplemented with an arbitrary or tabulated equation of state. The proposed approximation technique is robust, formally second-order accurate in space,…

Numerical Analysis · Mathematics 2023-02-22 Bennett Clayton , Jean-Luc Guermond , Matthias Maier , Bojan Popov , Eric J. Tovar

We present an implicit-explicit finite volume scheme for two-fluid single-temperature flow in all Mach number regimes which is based on a symmetric hyperbolic thermodynamically compatible description of the fluid flow. The scheme is stable…

Numerical Analysis · Mathematics 2023-12-15 Mária Lukáčová-Medvid'ová , Ilya Peshkov , Andrea Thomann

We consider the compressible Euler system for ideal gas flow in the absence of any forces except the internal thermodynamic pressure. In this setting, and in dimensions higher 1, it is known that wave-focusing can drive Euler solutions to…

Analysis of PDEs · Mathematics 2026-04-27 Helge Kristian Jenssen

The unified gas kinetic scheme (UGKS) of K. Xu et al. [K. Xu and J.-C. Huang, J. Comput. Phys., 229, pp. 7747--7764, 2010], originally developed for multiscale gas dynamics problems, is applied in this paper to a linear kinetic model of…

Numerical Analysis · Mathematics 2014-01-24 Luc Mieussens

We address a class of schemes for the Euler equations with the following features: the space discretization is staggered, possible upwinding is performed with respect to the material velocity only and the internal energy balance is solved,…

Numerical Analysis · Mathematics 2020-06-25 R. Herbin , J. -C. Latché , S. Minjeaud , N. Therme