Characteristic Method for One-Dimensional Scalar Hyperbolic Conservation Lawswith Stiff Source Terms

摘要

The authors consider the initial value problem for scalar hyperbolic conservationlaws in one space dimension, with (stiff) source terms. The source term admits 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. An implicit numerical method is introduced which produces discontinuities propagating at the correct speed. It is proved that this method preserves monotone profiles and an estimate for the global discretization error is given. The numerical results illustrate the correct behavior of this method.