相关论文: An asymptotic preserving scheme for the relativist…
Large weak solutions to Navier--Stokes--Maxwell systems are not known to exist in their corresponding energy space in full generality. Here, we mainly focus on the three-dimensional setting of a classical incompressible…
We investigate a projective integration scheme for a kinetic equation in the limit of vanishing mean free path, in which the kinetic description approaches a diffusion phenomenon. The scheme first takes a few small steps with a simple,…
We consider the compressible Euler equations of gas dynamics with isentropic equation of state. Standard numerical schemes for the Euler equations suffer from stability and accuracy issues in the low Mach regime. These failures are…
The radiation magnetohydrodynamics (RMHD) system couples the ideal magnetohydrodynamics equations with a gray radiation transfer equation. The main challenge is that the radiation travels at the speed of light while the magnetohydrodynamics…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
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…
We study the long-time asymptotic of the solutions to Maxwell's equation in the case of a upper-hybrid resonance in the cold plasma model. We base our analysis in the transfer to the time domain of the recent results of B. Despr\'es, L.M.…
We show that the simplified $3D$ relativistic Vlasov-Maxwell (sRVM) system, in which there is no magnetic field, poses a global solution for a class of arbitrarily large cylindrically symmetric initial data. In particular, a vanishing order…
We consider multi-dimensional extensions of Maxwell's seminal rheo-logical equation for 1D viscoelastic flows. We aim at a causal model for compressible flows, defined by semi-group solutions given initial conditions , and such that…
This paper presents a grid-free simulation algorithm for the fully three-dimensional Vlasov--Poisson system for collisionless electron plasmas. We employ a standard particle method for the numerical approximation of the distribution…
We study two relaxation problems in the class of partially dissipative hyperbolic systems: the compressible Euler system and the compressible Euler-Maxwell system. In classical Sobolev spaces, we derive a global convergence rate of…
Previously developed method for finding asymptotic solutions of Vlasov equations using two-dimensional (in coordinate x and time t) Laplace transform is here applied to consider transversal oscillations and waves in low-collision…
We study the implicit upwind finite volume scheme for numerically approximating the linear continuity equation in the low regularity DiPerna-Lions setting. That is, we are concerned with advecting velocity fields that are spatially Sobolev…
Recent development of structure-preserving geometric particle-in-cell (PIC) algorithms for Vlasov-Maxwell systems is summarized. With the arriving of 100 petaflop and exaflop computing power, it is now possible to carry out direct…
We introduce a new family of paraxial asymptotic models that approximate the Vlasov-Maxwell equations in non-relativistic cases. This formulation is $n$-th order accurate in a parameter $\eta$, which denotes the ratio between the…
We construct a new nonlinear finite volume (FV) scheme for highly anisotropic diffusion equations, that satisfies the discrete minimum-maximum principle. The construction relies on the linearized scheme satisfying less restrictive…
The time evolution of a collisionless plasma is modeled by the Vlasov-Maxwell system which couples the Vlasov equation (the transport equation) with the Maxwell equations of electrodynamics. We only consider a 'two-dimensional' version of…
The Vlasov equation is a nonlinear partial differential equation that provides a first-principles description of the dynamics of plasmas. Its linear limit is routinely used in plasma physics to investigate plasma oscillations and stability.…
We consider the 1/2-dimensional relativistic Vlasov-Maxwell system that describes the time-evolution of a plasma. We find a relatively simple criterion for spectral instability of a wide class of equilibria. This class includes…
A new type of systematic approach to study the incompressible Euler equations numerically via the vanishing viscosity limit is proposed in this work. We show the new strategy is unconditionally stable that the $L^2$-energy dissipates and…