A Robust Least Squares Kinetic Upwind Scheme for Euler equations

Abstract

A new second order accurate grid-free scheme called Least Squares Kinetic Upwind Method (LSKUM) for the solution of Euler Equations has been developed. This method works just on a distribution of points and only the local connectivity information at each node needs to be stored. Weighted least squares method has been used to obtain the discrete approximation of the spatial derivatives. Then upwinding is done by appropriately choosing the weights. This method is made second order accurate by a two step formula. In this kinetc upwind method, both Kinetic Flux Vector Splitting (KFVS) and Pecular Velocity based Upwinding (PVU) are used to obtain results for a wide range of two dimensional flow problems. These results demonstrate amply the capability and the robustness of the present method.