Development of a High-Resolution Scheme for a Multi-dimensional Advection-Diffusion Equation
Journal
Journal of Computational Physics
Journal Volume
144
Journal Issue
1
Pages
1-16
Date Issued
1998
Author(s)
Abstract
In this article, we present a composite scheme to solve the scalar transport equation in a two-dimensional space. The aim of this study is to accurately resolve sharp profiles in the flow. The theory of the M-matrix serves as the theoretical foundation for achieving this goal. Attempts to extend the approach to resolve discontinuities in all cases motivate the development of the composite scheme. For this study, a conditionally monotonic Legendre polynomial finite element model is used together with an unconditionally monotonic scheme. Computational evidence reveals that the composite model improves stability while it maintains accuracy. The application scope is thus greatly extended. © 1998 Academic Press.
Type
journal article