A Very Easy High-Order Well-Balanced Reconstruction for Hyperbolic Systems with Source Terms

A Well-Balanced Path-Integral f-Wave Method for Hyperbolic Problems with Source Terms

Systems of hyperbolic partial differential equations with source terms (balance laws) arise in many applications where it is important to compute accurate time-dependent solutions modeling small perturbations of equilibrium solutions in which the source terms balance the hyperbolic part. The f-wave version of the wave-propagation algorithm is one approach, but requires the use of a particular a...

A Well-balanced Scheme Using Non-conservative Products Designed for Hyperbolic Systems of Conservation Laws with Source Terms

The aim of this paper is to present a new kind of numerical processing for hyperbolic systems of conservation laws with source terms. This is achieved by means of a non-conservative reformulation of the zero-order terms of the right-hand-side of the equations. In this context, we decided to use the results of DalMaso, LeFloch and Murat 9] about non-conservative products, and the generalized Roe...

Stii Well{posedness for Hyperbolic Systems with Large Relaxation Terms

The Cauchy problem for linear constant{coeecient hyperbolic systems u t + Au x = (1==)Bu is analyzed. Here (1==)Bu is a large relaxation term, and we are mostly interested in the critical case where B has a non{trivial nullspace. A concept of stii well{posedness is introduced that ensures solution estimates independent of 0 < 1. Under suitable assumptions, we prove convergence of the L 2 {solut...

High-order Well-balanced Schemes

Explicit Finite Volume Schemes of Arbitrary High Order of Accuracy for Hyperbolic Systems with Stiff Source Terms

In this article we propose a new class of finite volume schemes of arbitrary accuracy in space and time for systems of hyperbolic balance laws with stiff source terms. The new class of schemes is based on a three stage procedure. First, in order to achieve high order accuracy in space, a nonlinear weighted essentially non-oscillatory reconstruction procedure is applied to the cell averages at t...