New non-oscillatory central schemes on unstructured triangulations for hyperbolic systems of conservation laws

  • Authors:

  • Ivan Christov;Bojan Popov

  • Affiliations:

  • Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA;Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2008

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Abstract

We discuss an extension of the Jiang-Tadmor and Kurganov-Tadmor fully-discrete non-oscillatory central schemes for hyperbolic systems of conservation laws to unstructured triangular meshes. In doing so, we propose a new, ''genuinely multidimensional,'' non-oscillatory reconstruction-the minimum-angle plane reconstruction (MAPR). The MAPR is based on the selection of an interpolation stencil yielding a linear reconstruction with minimal angle with respect to the horizontal. This means that the MAPR does not bias the solution by using a coordinate direction-by-direction approach to the reconstruction, which is highly desirable when unstructured meshes consisting of elements with (almost) arbitrary geometry are used. To show the ''black-box solver'' capabilities of the proposed schemes, numerical results are presented for a number of hyperbolic systems of conservation laws (in two spatial dimensions) with convex and non-convex flux functions. In particular, it is shown that, even though the MAPR is neither designed with the goal of obtaining a scheme that satisfies a maximum principle in mind nor is total-variation diminishing (TVD), it provides a robust non-oscillatory reconstruction that captures composite waves accurately.