A TVD-type method for 2D scalar Hamilton-Jacobi equations on unstructured meshes

Authors:
Lingyan Tang;Songhe Song
Affiliations:
Department of Mathematics and System Science, Science School, National University of Defense Technology, Changsha, Hunan, China;Department of Mathematics and System Science, Science School, National University of Defense Technology, Changsha, Hunan, China
Venue:
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
Year:
2006

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Abstract

In this paper, a TVD-type difference scheme which satisfies maximum principle is developed for 2D scalar Hamilton-Jacobi equations on unstructured triangular meshes. The main ideas are node-based approximations and derivative-limited reconstruction with quadratic interpolation polynomial. The solution's slope satisfies maximum principle. Numerical experiments are performed to demonstrate high-order accuracy in smooth fields and good resolution of derivative singularities. The new method is simpler than WENO.