相关论文: A second order positivity preserving well-balanced…

We consider the periodic problem for two-fluid non-isentropic Euler-Maxwell systems in plasmas. By means of suitable choices of symmetrizers and an induction argument on the order of the time-space derivatives of solutions in energy…

High order schemes are known to be unstable in the presence of shock discontinuities or under-resolved solution features for nonlinear conservation laws. Entropy stable schemes address this instability by ensuring that physically relevant…

The present work proposes a well-balanced finite volume-type numerical method for the solution of non-conservative hyperbolic partial differential equations (PDEs) with source terms. The method is characterized, first, by the use of a…

We propose and study a fully discrete finite volume scheme for the Vlasov-Fokker-Planck equation written as an hyperbolic system using Hermite polynomials in velocity. This approach naturally preserves the stationary solution and the…

The Euler-Maxwell system as a hydrodynamic model for plasma physics to describe the dynamics of the compressible electrons in a constant charged non-moving ion background is studied. The global smooth flow with small amplitude is…

We address here the discretization of the momentum convection operator for fluid flow simulations on 2D triangular and quadrangular meshes and 3D polyhedral meshes containing hexahedra, tetrahedra, prisms and pyramids. The finite volume…

The stochastic logistic model with regime switching is an important model in the ecosystem. While analytic solution to this model is positive, current numerical methods are unable to preserve such boundaries in the approximation. So,…

This article proposes a highly accurate and conservative method for hyperbolic systems using the finite volume approach. This innovative scheme constructs the intermediate states at the interfaces of the control volumes using the method of…

Non-local systems of conservation laws play a crucial role in modeling flow mechanisms across various scenarios. The well-posedness of such problems is typically established by demonstrating the convergence of robust first-order schemes.…

In this paper, we construct a robust adaptive central-upwind scheme on unstructured triangular grids for two-dimensional shallow water equations with variable density. The method is well-balanced, positivity-preserving, and oscillation-free…

We present a semi-discrete finite volume scheme for the local NavierStokes-Korteweg and Euler-Korteweg systems. Our scheme is applicable for equidistant Cartesian meshes in one and two space dimensions. In contrast to other works, which…

This article is concerned with the analysis of the one-dimensional compressible Euler equations with a singular pressure law, the so-called hard sphere equation of state. The result is twofold. First, we establish the existence of bounded…

The hydrostatic equilibrium state is the consequence of the exact hydrostatic balance between hydrostatic pressure and external force. Standard finite volume or finite difference schemes cannot keep this balance exactly due to their…

Following Arnold's geometric interpretation, the Euler equations of an incompressible fluid moving in a domain D are known to be the optimality equation of the minimizing geodesic problem along the group of orientation and volume preserving…

This paper presents the construction of two numerical schemes for the solution of hyperbolic systems with relaxation source terms. The methods are built by considering the relaxation system as a whole, without separating the resolution of…

We propose a second order finite volume scheme for nonlinear degenerate parabolic equations. For some of these models (porous media equation, drift-diffusion system for semiconductors, ...) it has been proved that the transient solution…

In this work, we propose a positivity-preserving scheme for solving two-dimensional advection-diffusion equations including mixed derivative terms, in order to improve the accuracy of lower-order methods. The solution to these equations, in…

In this paper, we analyze a semi-discrete finite volume scheme for the three-dimensional barotropic compressible Euler equations driven by a multiplicative Brownian noise. We derive necessary a priori estimates for numerical approximations,…

We study the initial value problem for a kind of Euler equation with a source term. Our main result is the existence of a globally-in-time weak solution whose total variation is bounded on the the domain of definition, allowing the…

The fundamental "two-fluid" model for describing plasma dynamics is given by the Euler-Maxwell system, in which compressible ion and electron fluids interact with their own self-consistent electromagnetic field. We prove global stability of…