Numerical Wave Speed for One-Dimensional Scalar Hyperbolic Conservation Laws withSource Terms

摘要

In this paper we consider initial value problems for scalar hyperbolicconservation laws in one space dimension, with source terms. The source terms admit at least two equilibrium states as solutions of the underlying characteristic equation, one unstable and one stable. An essential numerical difficulty for this initial value problem is that numerical reaction waves are propagating at non-physical wave speeds. In this paper we consider two types of model problems, namely the ignition model and the Arrhenius' model. Applications include reactive gas dynamics, where chemical reactions between the constituent gases need to be modeled along with the fluid dynamics. The numerical solution is computed with a first order splitting method. For this method a detailed analysis of the numerical wave speed is given. Expressions are derived for the numerical wave speed, which explain the occurrence of non-physical wave speeds. Furthermore, convergence of the numerical speed to the exact speed is shown.