DEVELOPMENT OF A HIGH-RESOLUTION SCHEME FOR A MULTIDIMENSIONAL ADVECTION-DIFFUSION EQUATION

In this article, we present a composite scheme to solve the scalar tra nsport equation in a two-dimensional space. The aim of this study is t o accurately resolve sharp profiles in the flow. The theory of the M-m atrix serves as the theoretical foundation for achieving this goal. At tempts to extend the approach to resolve discontinuities in all cases motivate the development of the composite scheme. For this study, a co nditionally monotonic Legendre polynomial finite element model is used together with an unconditionally monotonic scheme. Computational evid ence reveals that the composite model improves stability while it main tains accuracy. The application scope is thus greatly extended. (C) 19 98 Academic Press.