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On the Numerical Solution of Conservation Laws by Minimizing Residuals

✍ Scribed by R.B. Lowrie; P.L. Roe

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 220 KB
Volume: 113
Category: Article
ISSN: 0021-9991
DOI: 10.1006/jcph.1994.1137

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✦ Synopsis

The numerical solution of conservation laws by minimizing the residuals of an overdetermined set of discrete equations is studied. Previous research has shown that for certain formulations, minimizing the residuals in the (L), norm will yield solutions that resolve discontinuities that are very sharp and correctly placed. In this study, we analyze a previously proposed method that numerically solves the (2 \mathrm{D}) advection equation with discontinuous data. The method is able to resolve the discontinuity over one mesh cell, without generating spurious oscillations. However, we have found that incorrect solutions are generated for some data. This had led us to formulate and prove two theorems concerning these results. We also provide an analysis of the solution procedure, along with suggestions for developing future schemes that are more applicable to a wide range of problems. (C) 1994 Academic Press. Inc.

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