A multiresolution finite volume scheme for two-dimensional hyperbolic conservation laws

Authors:
Lingyan Tang;Songhe Song
Affiliations:
Department of Mathematics and System Science, Science School, National University of Defense Technology, Changsha, Hunan 410073, China;Department of Mathematics and System Science, Science School, National University of Defense Technology, Changsha, Hunan 410073, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

In this paper, high-resolution finite volume schemes are combined with an adaptive mesh technique inspired by multiresolution analysis to improve the computational efficiency for two-dimensional hyperbolic conservation laws. The method is conservative. Moreover, it is stable which is proven numerically in this paper. The computational grid is dynamically adapted so that higher spatial resolution is automatically allocated to regions where strong gradients are observed. Using this proposed scheme, we compute several two-dimensional model problems and a compressive rate ranging from about 5-10 is observed in all simulations.