Mapped WENO and weighted power ENO reconstructions in semi-discrete central schemes for Hamilton-Jacobi equations

Authors:
Steve Bryson;Doron Levy
Affiliations:
NASA Advanced Supercomputing Division, NASA Ames Research Center, Moffett Field, CA;Department of Mathematics, Stanford University, Stanford, CA
Venue:
Applied Numerical Mathematics - Numerical methods for viscosity solutions and applications
Year:
2006

Citing 18
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Abstract

We incorporate new high-order WENO-type reconstructions into Godunov-type central schemes for Hamilton-Jacobi equations. We study schemes that are obtained by combining the Kurganov-Noelle-Petrova flux with the weighted power ENO and the mapped WENO reconstructions. We also derive new variants of these reconstructions by composing the weighted power ENO and the mapped WENO reconstructions with each other. While all schemes are, formally, fifth-order accurate, we show that the quality of the approximation does depend on the particular reconstruction that is being used. In certain cases, it is shown that the approximate solution may not converge to the viscosity solution at all.