Gridless Type Solver

Abstract

A gridless type solver, an alternative to conventional finite difference methods, has been developed for the Navier-Stoke equations. Points, instead of grids, are first distributed over the computational domain considered. The spatial derivatives of flow quantities are evaluated at each point with linear combinations of certain coefficients and the quantities in its cloud of points. An upwind method may be obtained using Roe’s approximate Riemann solver for evaluating the inviscid flux. The linear system derived from an implicit Euler temporal discretization is solved using a LU-SGS method. The solver can work fairly well on the points of any kind of grids and even on points arbitrarily distributed over the computational domains. The flexibility and reliability of the present method are demonstrated for representative test cases of subsonic, transonic, and supersonic flows.