A Second Order Central Scheme for Hamilton-Jacobi Equations on Triangular Grids

Authors:
Peter Popov;Bojan Popov
Affiliations:
Institute for Scientific Computation, Texas A&M University, College Station, USA TX-77843;Department of Mathematics, Texas A&M University, College Station, USA TX-77843
Venue:
Numerical Analysis and Its Applications
Year:
2009

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Abstract

In this paper, we describe a Godunov-type fully discrete scheme for Hamilton-Jacobi equations on triangular meshes. This scheme is an extension of the Lin-Tadmor and Kurganov-Tadmor fully discrete nonoscillatory central schemes to unstructured triangular meshes. In this new construction, we propose a new, "genuinely multidimensional", nonoscillatory reconstruction. The construction is simple, universal and deviates from the existing high-order extensions of the central and central-upwind schemes for Hamilton-Jacobi equations.