On the Total Variation of High-Order Semi-Discrete Central Schemes for Conservation Laws

Authors:
Steve Bryson;Doron Levy
Affiliations:
NASA Advanced Supercomputing Division, NASA Ames Research Center, Moffett Field, USA 94035-1000;Department of Mathematics, Stanford University, Stanford, USA 94305-2125
Venue:
Journal of Scientific Computing
Year:
2006

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Abstract

We discuss a new fifth-order, semi-discrete, central-upwind scheme for solving one-dimensional systems of conservation laws. This scheme combines a fifth-order WENO reconstruction, a semi-discrete central-upwind numerical flux, and a strong stability preserving Runge---Kutta method. We test our method with various examples, and give particular attention to the evolution of the total variation of the approximations.