曲边单元间断有限元方法求解二维Euler方程

摘要

考虑到间断有限元方法对边界的敏感性,采用基于八节点曲边四边形单元的间断有限元方法求解了Euler方程的圆柱绕流问题.详细推导了八节点四边形单元的变换关系,给出了Jacobi矩阵行列式的具体表达式.对比直边单元和曲边单元的计算结果,采用曲边单元后,计算结果符合Euler方程的无粘假设,得出了八节点四边形单元间断有限元方法求解Euler方程是合适的结论.%Considering the sensitivity of the discontinuous finite element method to the boundary, we have solved the problem of flow around a cylinder of Euler equation with the discontinuous finite element method based on 8 nodes curved boundary quadrilateral element.We deduce the transformation of the 8 node curved boundary quadrilateral element, and give the expression of the determinant of the Jocabi matrix.By comparing the different result from straight element and curved element,it is found that the result is true for Euler equation by using curve element, and it is reasonable to use the discontinuous finite element method based on 8 nodes curved boundary quadrilateral element to solve Euler equation.