间断Galerkin有限元和有限体积混合计算方法研究

通过局部坐标变换而建立的非正交单元间断Galerkin(DG)有限元计算方法计算精度高， 但计算量大、内存需求大；而非结构网格有限体积方法虽然准确计算热流的问题目 前还没有完全解决，但其具有计算速度快和内存需求小的优点. 该研究是将有 限元和有限体积方法的优点结合，发展有限元和有限体积的混合方法. 在物面 附近黏性占主导作用的区域内采用有限元方法进行计算，在远离物面的区域采用快速的有限 体积方法进行计算，在有限元和有限体积方法结合处要保证通量守恒. 通过算例说明有 限元和有限体积混合方法既能保证黏性区域的热流计算精度和流场结构的分辨率，又能 降低内存需求和提高计算效率，使有限元方法应用于复杂外形(实际工程问题)的计 算成为可能.

A FINITE ELEMENT/FINITE VOLUME MIXED SOLVER ON HYBRID GRIDS

The Discontinuous Galerkin (DG) finite element methods (FEM) have shown to be of high-accuracy for simulating complex flows with shock waves, especially viscous effects near boundary layers. However, they require more CPU time and memory storage than finite volume methods. On the other hand, the finite volume methods face the difficulty of predicting the heat flux over complex geometries, especially on unstructured grids. An optimal choice is to combine the two kinds of methods to take all their advantages. So in this paper, a finite element/finite volume mixed solver is presented. Within the mixed solver, the previous DG-FEM solver on non-orthogonal grids is used near the boundary layers to capture the viscous effects, while the finite volume solver is adopted in the outer field to save the CPU time and memory storage. The numerical flux on the interface of FE/FV solvers is solved conservatively to guarantee the transformation of FE/FV solvers smoothly. The mixed solver is validated by two hypersonic cases, e.g. hypersonic flows over a blunt cone and double-ellipsoids. The computational results, including flow patterns and heat flux distributions, show good agreements with experimental data, and the comparison on CPU time and memory storage demonstrates the higher efficiency over the finite element solver.