A novel three-dimensional Cartesian cut cell algorithm,referred to as 6+N,is proposed to describe and treat arbitrary three-dimensional Kitta Cube.This method can avoid the enumeration for millions of cutting patterns and implement the discretization and solution of the N-S equations in a unified form.The present method is applied to simulate natural convection heat transfer in an annular tunnel between two concentric or eccentric spheres.The numerical results show that Kitta Cube can express curve surfaces accurately with an error of less than 1.0%.The accuracy of solutions obtained by the present method is approximately equivalent to that by the body-fitted method.In addition,higher overall heat transfer coefficients can be achieved by lowering the position of the inner sphere for eccentric arrangement.

An adaptive unstructured grid generation algorithm,which adopts Cartesian grid to decompose 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 equations 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 collocated variables arrangement. The present method is applied to two benchmark problems and is verified to be accurate and efficient.

以四叉树非结构化网格为基础,提出了背景区域采用正方形四叉树网格、边界区域采用切削网格的一种可以表达复杂几何形状的网格生成方法,该网格具有生成过程简单,正交性好等优点.在这种网格的基础上,采用非结构网格有限体积法进行离散得到了多种形状切削网格并存时Navier-stokes(N-S)方程的求解算法,并以顶盖驱动斜方腔流和方腔内热圆柱自然对流为例,应用上述算法实现了网格生成和流动数值模拟,与基准解进行了比较,一致性较好.计算结果表明这种切削网格方法及其N-S方程求解方法具有可靠性和应用前景.