二维欧拉方程在非结构网格上的自适应有限元算法

 发展了一种易于和自适应网格加密技术相结合的非结构三角形网格生成技术。这种方法的特点是域内节点可任意规定；根据欧拉方程解的误差估计,在流场某些区域增加节点后,能重新快速生成新的具有高质量三角形单元的非结构网格。欧拉方程采用Ｇａｌｅｒｋｉｎ空间离散和Ｒｉｃｈｔｍｙｅｒ两步显式时间推进相结合的有限元法求解,并以沿流线熵的变化量作为物理判据进行网格自适应加密,提高解的精度。

ADAPTIVE FINITE ELEMENT METHOD FOR FULER EQUATIONS ON UNSTRUCTURED MESHES

A technique of nonstructured triangular mesh generation which is easy to be incor-porated in the technique of self adaptive mesh refinement is developed. The distinguished fea-ture of the present method is that the hiesh points inside the domain can be prescribed arbitrarily and thus a new nonstructured triangular mesh with good triangular quality will be generat-ed quickly after the required nodes have been added in the region where the mesh has to be refined based on the error estimate of the solution of Euler equation. The Galerkin spatial dis-cretization in combination with a two step Richtmyer explicit time marching flnite element al-gorithm is adopted to solve the Euler equation and the variatiOn of the entropy increment along the stream direction is used as the physical criteria for self adaptive mesh refinement to reduce the numerical error and raise the accuracy of solutions.