A TVD finite difference scheme with non-uniform meshes and without upstream weighting

Glaister, P. (1991) A TVD finite difference scheme with non-uniform meshes and without upstream weighting. Computers & Mathematics with Applications, 22 (3). pp. 45-58. ISSN 0898-1221 doi: 10.1016/0898-1221(91)90069-G

Abstract/Summary

We present a finite difference scheme, with the TVD (total variation diminishing) property, for scalar conservation laws. The scheme applies to non-uniform meshes, allowing for variable mesh spacing, and is without upstream weighting. When applied to systems of conservation laws, no scalar decomposition is required, nor are any artificial tuning parameters, and this leads to an efficient, robust algorithm.