统一坐标系下可压缩流体的间断有限元方法研究

本项目主要针对可压缩流体力学问题,研究统一坐标系下适用于多介质流和自由面问题数值模拟、高精度和高分辨率的Runge-Kutta间断Galerkin有限元方法和Runge-Kutta控制体积间断有限元方法。充分发挥统一坐标系的灵活性和间断有限元方法的优点，在二维结构和非结构网格上完成统一坐标系下利用间断有限元方法求解气动方程组的计算程序，初步开展统一坐标系下求解三维气动方程组的间断有限元方法研究。研制这些算法的相应软件，为航空航天、高温高压物理研究、燃烧机理和爆炸效应利用等问题的数值模拟提供高效和高置信度的计算方法及应用软件。

In this project, we construct the high accuracy and high resolution Runge-Kutta discontinuous Galerkin finite element method and Runge-Kutta control volume discontinuous finite elment method for gas dynamic equations in unified coordinate, which can be used in multi-medium fluid and free surface fluid simulations. We proposed to complete the corresponding pragramm for solving gas dynamic equations in unified coordinate on two dimensional structed and unstructed meshes. Then we will start the preliminary research on discontinuous finite element method for three dimensional gas dynamic equations. Such methods can combine the advantages of the discontinuous finite element method and the flexibility of the unified coordinate. We develop the corresponding software, which can be used in numerical simulations in the areas of aerospace, high temperature and high pressure physics, combustion mechanism, the use of explosive effects and other issues.