Conditionally Stable Multidimensional Schemes for Advective Equations

Authors:
Adrian Sescu;Abdollah A. Afjeh;Ray Hixon;Carmen Sescu
Affiliations:
MIME Department, University of Toledo, Toledo, USA 43606;MIME Department, University of Toledo, Toledo, USA 43606;MIME Department, University of Toledo, Toledo, USA 43606;MIME Department, University of Toledo, Toledo, USA 43606
Venue:
Journal of Scientific Computing
Year:
2010

Citing 10
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Abstract

It is shown that the isotropic wave-like multidimensional spatial stencils combined with linear multistep and Runge-Kutta time marching schemes provide more favorable stability restrictions for advective initial-value problems. Under certain conditions the maximum allowable time step can be doubled compared to using conventional spatial stencils. Consequently, this paper shows that the multidimensional optimizations of spatial schemes, involving more grid points, are not inherently less efficient in terms of the processing time. Three numerical tests solving the two and three dimensional advection equations are carried out to experiment the stability restrictions found in the previous sections.