隐式无网格算法及其应用研究

本文的主要目的在于研究求解Euler方程的隐式无网格算法，并应用于复杂的流场计算。采用无网格算法，计算区域用点云离散代替通常的网格划分；计算点上的空间导数，用当地点云上引入的二次极小曲面逼近。求解的Euler方程用隐式时间后差离散，结合用Roe的近似Riemann解确定通量，并用LU－SGS算法分步计算，数值求解了单翼型或双翼型模拟的复杂绕流。

An implicit gridless method and its applications

The main goal of this paper is to study an implicit gridless method for solution of the Euler equations with the application to complicated flow fields. Clouds of points distributed all over the computational domain are adopted instead of mesh generation. The spatial derivatives are directly approximated by using local least squares 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 complicated flows over one or two staggered airfoils.