On large time step Godunov scheme 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...

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

Convergence of Godunov-Type Schemes for Scalar Conservation Laws under Large Time Steps

In this paper, we consider convergence of classical high order Godunov-type schemes towards entropy solutions for scalar conservation laws. It is well known that sufficient conditions for such convergence include total variation boundedness of the reconstruction and cell or wavewise entropy inequalities. We prove that under large time steps, we only need total variation boundedness of the recon...

A Central Weno-tvd Scheme for Hyperbolic Conservation Laws

The purpose of this paper is to carry out a modification of the finite volume WENO (weighted essentially non-oscillatory) scheme of Titarev and Toro [10]. This modification is done by using the third order TVD flux [10] as building blocks in spatially fifth order WENO schemes, instead of the second order TVD flux proposed by Titarev and Toro. The resulting scheme improves both the original and ...

A Genuinely Multi-dimensional Relaxation Scheme for Hyperbolic Conservation Laws

A new genuinely multi-dimensional relaxation scheme is proposed. Based on a new discrete velocity Boltzmann equation, which is an improvement over previously introduced relaxation systems in terms of isotropic coverage of the multi-dimensional domain by the foot of the characteristic, a finite volume method is developed in which the fluxes at the cell interfaces are evaluated in a genuinely mul...