High Resolution Schemes for Conservation Laws With Source Terms.

2008

This memoir is devoted to the study of the numerical treatment of source terms in hyperbolic conservation laws and systems. In particular, we study two types of situations that are particularly delicate from the point of view of their numerical approximation: The case of balance laws, with the shallow water system as the main example, and the case of hyperbolic equations with stiff source terms. In this work, we concentrate on the theoretical foundations of highresolution total variation diminishing (TVD) schemes for homogeneous scalar conservation laws, firmly established. We analyze the properties of a second order, flux-limited version of the Lax-Wendroff scheme which avoids oscillations…