The goal of this work is to introduce new families shock-capturing high-order numerical methods for systems conservation laws that combine Fast WENO (FWENO) and Optimal (OWENO) reconstructions with Approximate Taylor the time discretization. FWENO are based on smoothness indicators require a lower number calculations than standard ones. OWENO definition nonlinear weights allows one unconditiona...

Abstract Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical to solve steady-state solutions hyperbolic partial differential equations (PDEs). The Gauss-Seidel iterations and alternating strategy used cover characteristics PDEs in each order achieve convergence rate solutions. A nice property fixed-point which distinguishes them from other is that they explicit ...

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 ...

ADER schemes are numerical methods, which can reach an arbitrary order of accuracy in both space and time. They are based on a reconstruction procedure and the solution of generalized Riemann problems. However, for general boundary conditions, in particular of Dirichlet type, a lack of accuracy might occur if a suitable treatment of boundaries conditions is not properly carried out. In this wor...

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...

Single-stage or single-step high-order temporal discretizations of partial differential equations (PDEs) have shown great promise in delivering accuracy time with efficient use computational resources. There has been much success developing such methods for finite volume method (FVM) PDEs. The Picard Integral formulation (PIF) recently made single-stage accessible difference (FDM) discretizatio...

Abstract Conservation properties of iterative methods applied to implicit finite volume discretizations nonlinear conservation laws are analyzed. It is shown that any consistent multistep or Runge-Kutta method globally conservative. Further, it Newton’s method, Krylov subspace and pseudo-time iterations conservative while the Jacobi Gauss-Seidel not in general. If using an explicit a locally di...

The effects of using both directions and directional subdividing on adaptive gridembedding on the computational time and the number of grid points required for the same accuracy are considered. Directional subdividing is used from the beginning of the adaptation procedure without any restriction. To avoid the complication of unstructured grid, the semi-structured grid was used. It is used to so...