A class of hybrid DG/FV methods for conservation laws II: Two-dimensional cases

By comparing the discontinuous Galerkin (DG) methods, the k-exact finite volume (FV) methods and the lift collocation penalty (LCP) methods, a concept of 'static reconstruction' and 'dynamic reconstruction' was introduced for higher-order numerical methods in our previous work. Based on this concept, a class of hybrid DG/FV methods was presented for one-dimensional conservation law using a 'hybrid reconstruction' approach. In the hybrid DG/FV schemes, the lower-order derivatives of the piecewise polynomial are computed locally in a cell by the traditional DG method (called as 'dynamic reconstruction'), while the higher-order derivatives are re-constructed by the 'static reconstruction' of the FV method, using the known lower-order derivatives in the cell itself and in its adjacent face neighboring cells. In this follow-up paper, the hybrid DG/FV schemes are extended onto two-dimensional unstructured and hybrid grids. The two-dimensional linear and non-linear scalar conservation law and Euler equations are considered. Some typical cases are tested to demonstrate the performance of the hybrid DG/FV method, and the numerical results show that they can reduce the CPU time and memory requirement greatly than the traditional DG method with the same order of accuracy in the same mesh.