基于高阶物面近似的自适应间断有限元法欧拉方程数值模拟

摘要

将高阶间断有限元与网格自适应相结合，于非结构网格上求解二维 Euler 方程。将数值解多项式的高阶项贡献用人工粘性项系数的形式进行量化，网格自适应过程中以人工粘性项系数作为网格自适应的指示器。在系数达到设定的上限阀值的区域进行网格加密，在系数达到设定的下限阀值的区域将迭代过程中加密过的网格稀疏以减少网格量。所有自适应均在高阶曲线逼近真实物面的基础上进行，以保证数值结果的精度。典型数值算例结果与实验结果进行了对比，表明采用该自适应间断有限元法可以保证以尽可能小的计算量得到高精度结果。%A high-order discontinuous method (DGM)is integrated with adaptive method to solve Euler equations on unstructured mesh.Contribution of the polynomial ’s highest-order terms is quantified in the form of artificial viscous coefficient.The coefficient is regarded as the indicator of h-adaptivity.Elements where the coefficients are greater than the upper limit are re-fined.Those where the coefficients are less than the lower limit are coarsened if they have been refined.A high-order geometric approximation of curved boundaries is adopted to ensure the con-vergence.Numerical results of test cases are consistent with corresponding experimental ones. High accurate numerical results can be obtained with the h-adaptive method at low expense.