Finite Volume Methods on Quadrilateral and Moving Meshes

Abstract: The topic of this thesis is the study of finite volume methods for hyperbolic conservation laws on non-uniform meshes. A high-order hyperbolic reconstruction method is presented. The method is constructed for quadrilateral meshes, since more realistic hyperbolic problems involve more complicated problem domains than the standard rectangular ones. The method is an extension of the well known Piecewise Hyperbolic Method (PHM), which is known to yield sharp resolution around corners in the solution compared to other reconstruction methods of the same order. Furthermore, the method is applied in a moving mesh adaptive framework in order to better resolve discontinuities without increasing computational costs. The moving mesh method employed is further developed to work with higher order reconstructions.