Preprint 1998-024

Explicit Finite Difference Schemes for the Advection Equation

Abstract: Conventional explicit finite difference schemes for the advection equations are subject to the time step restrictions dictated by the CFL condition. In many situations, time step sizes are not chosen to satisfy accuracy requirements but rather to satisfy the CFL condition. In this paper we present explicit algorithms which are stable far beyond the CFL restriction. Similar or even better accuracy can be achieved with a much larger time step size. The idea is matching the stencil and the real domain of dependence by characteristic analysis. Numerical tests are done for linear advection equations as well as the Burgers equation.

Paper:

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Title:

Explicit finite difference schemes for the advection equation

Author(s):

Mike H. Zhou, mailto:Mike.Zhou@usm.edu

Michael Mascagni, http://www.math.ntnu.no/conservation/1998/mailtoMichael.Mascagni@usm.edu:

Alice Y. Qiao, mailto:Alice.Qiao@usm.edu

Publishing information:

Comments:

Submitted by:

mailto:Mike.Zhou@usm.edu June 17 1998.