Implicit Gridless Method for Euler Eguations

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.