自适应四叉树网格下的N-S方程数值求解模型

提出了一种自适应四叉树网格下的N-S方程数值求解模型.网格能够根据涡度值大小进行自动加密或合并,以达到在不显著增加计算量的前提下,提高重点区域分辨率的目的.模型中采用了无条件稳定的MacCormack格式计算对流项,采用修正的中心差分格式离散压力泊松方程,并提出了在树型网格下黏性项的变通离散格式.通过算例证明,利用新模型所得到的压力泊松方程的数值解具有二阶精度,速度解的精度超过一阶.计算得到的方腔流中轴线上速度分布与Ghia计算结果一致,圆柱绕流中拖曳力系数和升力系数与实测结果一致.方腔流算例还表明,在相同分辨率情况下采用自适应网格计算时间可减少近一半.

Numerical N-S Equation Solver Based on Adaptive Quadtree Mesh

A numerical N-S equation solver is presented based on the adaptive quadtree mesh, in which the grid size can be automatically adjusted according to the value of vorticity. In this way, the grid resolution of the interested area can be enhanced without significant increase of the computational time. An unconditionally stable MacCormack nu- merical scheme is adopted in the model for the advection term and a modified central difference scheme is introduced for the discretization of the Poisson equation. A modified difference scheme is proposed for the viscous term in quad- tree mesh frame. The computational results indicate that the numerical solution of the Poisson equation in the model is of second-order accuracy, and the numerical solution of velocity is beyond first-order accuracy. The velocity profile along the central axes in the example of the driven cavity flow agrees with that by Ghia. The drag coefficient and the lift coefficient in the example of flow over a circular cylinder are consistent with those of the experiment. The example of the driven cavity flow also shows that the computational time is effectively reduced by half with the adaptive mesh technique.