An efficient Legendre-Galerkin spectral element method for the steady flows in rectangular cavities
An efficient Legendre-Galerkin spectral element method for the steady flows in rectangular cavities
复制标题
矩形腔内稳定流动的高效Legendre-Galerkin谱元法
DOI：
10.1080/00207160.2019.1659962
复制
发表时间：
2020
影响因子：
1.8
通讯作者：
Sun Tao
中科院分区：
文献类型：
--
作者：
Zhang Jun;Jiao Jianjun;Lin Fubiao;Li Wulan;Sun Tao
本文提出了一种求解矩形腔内稳态流动的高效勒让德-伽辽金谱元方法。首先，利用奇点减法消除了角部矩形腔中双调和方程的奇点；然后构造了适当的内基函数和接口基函数，使其保持连续性。因此，将离散变分公式简化为具有块对角线和条件良好的系数矩阵的线性系统，可以用共轭梯度迭代法有效地求解。最后给出了数值算例，说明了数值方法的有效性。将该方法用于求解矩形空腔内蠕变流动，数值结果与有限差分法提供的基准稳态解进行了比较。
An efficient Legendre–Galerkin spectral element method for the steady flows in rectangular cavities is proposed in this paper. Firstly, we eliminate the singularity of biharmonic equation in rectangular cavity at the corner by the singularity substraction technique. Then we construct some appropriate interior basis functions and interface basis functions which maintain-continuity. Consequently, the discrete variational formulation is reduced to a linear system with block diagonal and well-conditioned coefficient matrix, which can be efficiently solved by the conjugate gradient iteration method. Finally, several numerical examples are given to show the effectiveness of our numerical method. The present method is used to solve the creeping flows in rectangular cavities, the numerical results are compared well with the benchmark steady solutions provided by the finite difference method.