Second order accurate upwind difference schemes for scalar conservation laws with source terms

Glaister, P. (1993) Second order accurate upwind difference schemes for scalar conservation laws with source terms. Computers & Mathematics with Applications, 25 (4). pp. 65-73. ISSN 0898-1221 doi: 10.1016/0898-1221(93)90249-U

Abstract/Summary

A second order accurate, characteristic-based, finite difference scheme is developed for scalar conservation laws with source terms. The scheme is an extension of well-known second order scalar schemes for homogeneous conservation laws. Such schemes have proved immensely powerful when applied to homogeneous systems of conservation laws using flux-difference splitting. Many application areas, however, involve inhomogeneous systems of conservation laws with source terms, and the scheme presented here is applied to such systems in a subsequent paper.