A Simplified TVD Finite Difference Scheme via Artificial Viscosity
SIAM Journal on Scientific and Statistical Computing1987Vol. 8(1), pp. 1–18
Citations Over TimeTop 17% of 1987 papers
Abstract
In this paper we show that the total variation diminishing (TVD) finite difference scheme which was analysed by Sweby [8] can be interpreted as a Lax-Wendroff scheme plus an upwind weighted artificial dissipation term. We then show that if we choose a particular flux limiter and remove the requirement for upwind weighting, we obtain an artificial dissipation term which is based on the theory of TVD schemes, which does not contain any problem dependent parameters and which can be added to existing MacCormack method codes. Finally, we conduct numerical experiments to examine the performance of this new method.
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