二维非结构网格生成及其数值模拟

Unstructured Grid Generation Algorithm and Its Numerical Simulations

提出一种二维非结构网格生成算法以及一种新的绕翼型的数值计算格式。首先,在Delaunay生成算法的框架下结合了阵面推进算法的优点,从覆盖整个计算区域的三角形着手,给出判断准则,由这些三角形的边直接生成新点,让新点与符合要求的三角形的边的两点相连构成三角形,这样生成的三角形网格具有较好的几何性质;其次,针对二维N0 0 1 2翼型跨声速绕流问题提出了一种新的计算格式。通过建立插值模板的概念,在每一个模板上运用最小二乘和MUSCL思想相结合的办法针对初始变量构造线性插值多项式,改进了原有的权系数的计算准则,将各插值多项式通过加权平均得到在整个模板集上通用的插值多项式,从而构造出高阶的有限体积格式;最后。

A new algorithm for generating an unstructured mesh and a new unstructured scheme in two dimensions is presented. Based on Delaunay triangulation and the advantages of advancing front type algorithms, a new algorithm is started from background mesh over the whole computation domain, generated by using advancing front type point placement, and uses Delaunay triangulation algorithm to constitute these points. The algorithm combines the advancing front type algorithm and Delaunay triangulation algorithm with the desired point distribution features, boundary integrity, etc. A new kind of monotone upstream-centered scheme for conser-vation lows (MUSCL)-type scheme for calculating transonic aerodynamic of the N0012 airfoil is proposed. Firstly, linear interpolating polynomials are constructed by using the thoughts of least-square and MUSCL ideas in the stencils, and their weight coefficients are determined to accommodate a normal polynomial in the stencil sets. Then, combining with the third order TVD Runge-Kutta time discretization, the third order scheme is obtained. Finally numerical tests show that the new scheme works well.