With study of finite volume(FV) methods and discontinuous Galerkin(DG) method,"static reconstruction" and "dynamic reconstruction" are proposed for high-order numerical schemes.Based on the concept of "hybrid reconstruction",a new class of hybrid DG/FV schemes is presented for two-dimensional(2D) unstructured grids to solve the 2D conservation law,including 2D scalar equations and Euler equations.In the hybrid DG/FV schemes,lower-order derivatives of the piecewise polynomial are computed locally in a cell by a traditional DG method(called "dynamic reconstruction"),and the higher-order derivatives are reconstructed by the "static reconstruction" of the FV method by using lower-order derivatives in the cell and immediate neighbour cells.Typical 2D cases are given,and accuracy study is carried out.Numerical results show that the hybrid DG/FV scheme reaches desired order of accuracy.In addition,the hybrid DG/FV scheme saves great CPU time and memory compared with same order DG schemes.

Multi-block patched grids in conjunction with a finite volume time domain (FVTD) algorithm are used to solve classic multi-body electromagnetic scattering problems. The governing equations of the Maxwell equations are cast into three-dimensional general curvilinear coordinates. The approach uses four-stage Runge-Kutta scheme for time integration and flux vector splitting based on eigen structure of flux Jacobian matrices for spatial discretization. Monotonic upstream shemes for conservation laws (MUSCL) scheme for interpolation is used for the dependent variable. The resolution for temporal discretization is second order and that for spatial discretization is third order. Numerical results for the radar cross section(RCS) of a classical configuration agree well with the analytical results. And the results for multi-body calculation agree well with that in references. It shows that the algorithm developed is able to simulate complex topology configuration (including multi-body) problems.