On a large time-step high resolution scheme

On a Large Time - Step High Resolution Scheme

This paper presents a class of new second-order accurate (IK + 3)-point explicit schemes for the computation of weak solutions of hyperbolic conservation laws, that are total-variation-diminishing under a CFL restriction of K. These highly nonlinear schemes are obtained by applying a nonoscillatory first-order accurate (IK + l)-point scheme to a modified flux. The so-derived second-order accura...

High-Resolution Large Time-Step Schemes for Hyperbolic Conservation Laws

On Large Time Step Godunov Scheme for Hyperbolic Conservation Laws

In this paper we study the large time step (LTS) Godunov scheme proposed by LeVeque for nonlinear hyperbolic conservation laws. As we known, when the Courant number is larger than 1, the linear interactions of the elementary waves in this scheme will be much more complicated than those for Courant number less than 1. In this paper, we will show that for scalar conservation laws, for any fixed C...

A total variation diminishing high resolution scheme for nonlinear conservation laws

In this paper we propose a novel high resolution scheme for scalar nonlinear hyperbolic conservation laws. The aim of high resolution schemes is to provide at least second order accuracy in smooth regions and produce sharp solutions near the discontinuities. We prove that the proposed scheme that is derived by utilizing an appropriate flux limiter is nonlinear stable in the sense of total varia...

A Weighted Essentially Nonoscillatory, Large Time-Step Scheme for Hamilton-Jacobi Equations

We investigate the application of weighted essentially nonoscillatory (WENO) reconstructions to a class of semi-Lagrangian schemes for first order time-dependent Hamilton–Jacobi equations. In particular, we derive a general form of the scheme, study sufficient conditions for its convergence with high-order reconstructions, and perform numerical tests to study its efficiency. In addition, we pro...