Abstract A number of physical processes in laser-plasma interaction can be described with the two-fluid plasma model. We report on a solver for three-dimensional model equations. This is particularly suited simulating between short laser pulses plasmas. The fluid relies two-step Lax–Wendroff split fourth-order Runge–Kutta scheme, and we use Pseudo-Spectral Analytical Time-Domain (PSATD) method ...

The discontinuous Galerkin (DG) or local discontinuous Galerkin (LDG) method is a spatial discretization procedure for convection-diffusion equations, which employs useful features from high resolution finite volume schemes, such as the exact or approximate Riemann solvers serving as numerical fluxes and limiters. The LaxWendroff time discretization procedure is an alternative method for time d...

We develop a high order finite difference numerical boundary condition for solving hyperbolic conservation laws on a Cartesian mesh. The challenge results from the wide stencil of the interior high order scheme and the fact that the boundary intersects the grids in an arbitrary fashion. Our method is based on an inverse Lax-Wendroff procedure for the inflow boundary conditions. We repeatedly us...

The goal of this article is to design robust and simple first order explicit solvers for one-dimensional nonconservative hyperbolic systems. These solvers are intended to be used as the basis for higher order methods for one or multidimensional problems. The starting point for the development of these solvers is the general definition of a Roe linearization introduced by Toumi in 1992 based on ...

We develop a theoretical tool to examine the properties of numerical schemes for advection equations. To magnify the defects of a scheme we consider a convection-reaction equation 0021-9 doi:10. q Th * Co E-m ut þ ðjujq=qÞx 1⁄4 u; u; x 2 R; t 2 Rþ; q > 1: It is shown that, if a numerical scheme for the advection part is performed with a splitting method, the intrinsic properties of the scheme a...

In [18], two of the authors developed a high order accurate numerical boundary condition procedure for hyperbolic conservation laws on a Cartesian mesh, which allows the computation using high order finite difference schemes on Cartesian meshes to solve problems in arbitrary physical domains whose boundaries do not coincide with grid lines. This procedure is based on the so-called inverse Lax-W...

In many application domains, the preferred approaches to the numerical solution of hyperbolic partial differential equations such as conservation laws are formulated as finite difference schemes. While finite difference schemes are amenable to physical interpretation, one disadvantage of finite difference formulations is that it is relatively difficult to derive the so-called goal oriented a po...