An Upwind Gridless Type Solver for Compressible Flows.

Abstract

An upwind gridless type solver has been developed for the compressible Euler and Navier-Stokes equations. Points are flrst distributed all over a computational domain. The spatial derivatives of the governing equations are estimated at each point using its cloud of points. An upwind method using Roe's approximate Riemann solver is adopted for the estimation of the inviscid flux. The linear system derived from temporal implicit approximation is solved using LU-SGS method. Validity of the solver has been examined with a series of numerical experiments for two-dimensional inviscid and viscous flows. The solver can work on structured grid points, locally refined Cartesian grid points, unstructured grid points, and any points distributed with arbitrary manners. The numerical results obtained for test cases, including flows over four-element airfoils, are in good agreement with corresponding exact solutions, available numerical results and experimental data.