A Bi-Hyperbolic Finite Volume Method on Quadrilateral Meshes

A non–oscillatory, high resolution reconstruction method on quadrilateral meshes in 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.