基于非正交同位网格下求解N-S方程的快速算法

Fast algorithm for solving N-S equation based on nonorthogonal collocated grids

利用有限体积法在非正交网格上实施了SIMPLEXT算法,该算法显式处理了邻点速度、源项及交叉导数项对速度修正值的影响,详细地给出了算法的推导过程,并对斜方腔顶盖驱动流进行了数值模拟。结果表明,在雷诺数不断增加的情况下,旋涡的数量也随之增加,同时意味着随着雷诺数的增大,惯性力也相对变大,从而对空腔内流动的作用也相应地增强,可见SIMPLEXT算法有效而准确地模拟了物理现象,同时能在相对宽的亚松弛因子上得到收敛解,具有更好的健壮性,可用于几何形状比较复杂流场的计算。

A SIMPLEXT algorithm is established based on nonorthogonal collocated grids by using finite volume method.The algorithm explicitly treats the influences of adjacent velocity,source term and cross-derivatives on the velocity correction value.Detail of derivation of the algorithm is given,and numerical simulation of the inclined lid-driven square cavity flow is carried out.Results show that as Reynolds number increases the number of eddy increases,the inertia force also increases that enhances the flow inside the cavity.It is demonstrated that convergent solution can be obtained by the SIMPLEXT algorithm under relatively wide underrelaxation.The robustness of the algorithm is also better and it can be used for the calculation of flow fields with complex boundaries.