中文摘要：

通过比较间断Galerkin有限元方法（DGM）和有限体积方法（FVM）,提出＂静态重构＂和＂动态重构＂的概念,进一步建立基于静动态＂混合重构＂算法的三阶DG/FV混合格式.在DG/FV混合格式中,单元平均值和一阶导数由DGM方法＂动态重构＂,二阶导数利用FVM方法＂静态重构＂;在此基础上,构造高阶多项式插值函数,得到三阶精度的DG/FV混合格式.将DG/FV混合格式推广应用于二维非结构网格,求解二维标量方程和Euler方程.典型算例数值实验表明,DG/FV混合格式达到了理想中的三阶精度.

英文摘要：

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 re-constructed 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.