柱体绕流的自适应数值模拟方法

Adaptive Numerical Simulation Method to Flows over Cube or Cylinder

发展了基于四叉树数据结构的网格生成和流动的Navier-Stokes方程数值求解器。采用压力梯度或者密度梯度的绝对值作为网格自适应的控制参量,同时采用基于最小二乘法的无网格方法处理对于一般Cartesian网格难于处理的物面边界条件。采取了绕方柱流动和绕圆柱流动的经典二维定常和非定常层流算例对所发展的方法进行了验证。计算的结果验证了所发展的方法在处理绕流流动时的合理性和有效性。从而也为将来数值模拟具有较复杂几何外形的流动提供了一种网格布局合理、高效,边界处理简单易行的新思路。

A quadtree-based adaptive Cartesian grid generation and flow solver of Navier-Stokes equations were developed.The grid adaptation based on pressure or density gradient was performed and a gridless or meshless method based on the least-square fashion was used to treat the wall surface boundary condition,which is generally difficult to be handled for the common Cartesian grid.First,to validate the technique of grid adaptation,the flows over a cube were computed.Second,the flows over the cylinder were calculated to validate the developed method.The computational results indicated the developed method is reasonable for complex flows.So this method provides a new idea to the simulation of flows over the objects with complex geometry figures and this method has the special characters of the more reasonable distribution of grids,the higher efficiency and the easier of boundary treatment.