A Bi-Hyperbolic Finite Volume Method on Quadrilateral Meshes

Authors:
H. J. Schroll;F. Svensson
Affiliations:
Centre for Mathematical Sciences, Lund University, Lund, Sweden SE---221 00;Centre for Mathematical Sciences, Lund University, Lund, Sweden SE---221 00
Venue:
Journal of Scientific Computing
Year:
2006

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Abstract

A non-oscillatory, high resolution reconstruction method on quadrilateral meshes in two dimensions (2D) is presented. It is a two-dimensional extension of Marquina's hyperbolic method. The generalization to quadrilateral meshes allows the method to simulate realistic flow problems in complex domains. An essential point in the construction of the method is a second order accurate approximation of gradients on an irregular, quadrilateral mesh. The resulting scheme is optimal in the sense that it is third order accurate and the reconstruction requires only nearest neighbour information. Numerical experiments are presented and the computational results are compared to experimental data.