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.

A technique on generation of unstructured grids for three dimensional complex geomtries is presented.Complex configurations are described by several typical kinds of surface patches.A 3D surface patch is first mapped to a 2D segment,then triangulated using a 2D grid generator based on the advancing front method,and finally mapped back to the original 3D shape.Tetrahedral grids are generated by an advancing front method and smoothed by a nodal relaxation technique and a Deluanay transformation.A mesh refinement technique is also given to obtain more accurate solutions.