一种求解N-S方程的自适应直角网格方法

提出了一种用直角网格表达背景、切削网格表达边界的非结构化自适应直角网格方法.该方法采用四叉树保存网格数据,将切削简化成6种类型,用速度的旋度和散度作为自适应加密标准,从而可实现任意二维区域网格的自动生成和自适应加密.通过将极小网格边界化处理,利用SIM-PLE算法处理速度和压力的耦合,实现了该网格上N-S方程的离散和求解.算例表明,该方法网格生成简单,可以用于任意形状上的流动和传热模拟,相比非自适应方法,用一半的网格数目即可达到相同的计算精度.

An Adaptive Cartesian Grid Method for the Incompressible Navier-Stokes Equations

An adaptive unstructured grid generation algorithm, which adopts Cartesian grid to de-compose a background domain and adopts a cut cell approach to express curvilinear boundaries, is presented for solving steady incompressible Navier-Stokes equations. By using quadtree data structure to store mesh data, simplifying cut types into six schemes, and employing the curl and divergence of velocity as criteria of grid refinement, this approach can implement mesh generation and adaptive refinement for arbitrary complex geometries automatically. A solution of N-S equa-tions via finite volume method for this mesh is derived. The SIMPLE based smoothing pressure correction is chosen to suppress the checkerboard pressure oscillation due to c0110cated variables arrangement. The present method is applied to two benchmark problems and is verified to be ac-curate and efficient.