求解Euler方程的隐式无网格算法

Implicit Gridless Method for Euler Equations

研究了求解Euler方程的隐式无网格算法.用点云离散计算区域,代替通常的网格划分;在当地点云上,引入二次平方极小曲面逼近计算空间导数;用Roe的近似Riemann解确定通量;并用LU SGS算法求解离散得到的Euler方程隐式时间后差联立方程组,数值模拟了二维翼型跨音速绕流.由于无网格算法区域离散只涉及点云,具有灵活性,适合处理复杂的气动外形.

An implicit gridless method is investigated for the Euler equations. Clouds of points distributed all over the computational domain are adopted instead of common mesh generation. The spatial derivatives are directly approximated by using local leastsquare curve fits in each cloud of points. An upwind method using Roe's approximate Riemann solver is used for the estimation of the inviscid flux. The linear system of the resulting backward Euler temporal discretization is computed by using LUSGS algorithm. The numerical implementations of the method are presented for transonic flows over 2D airfoils, which reveals the flexibility of using clouds of points for complicated aerodynamic shapes.