Accuracy and Robustness of Kinetic Meshfree Method

Summary

Meshfree methods are gaining popularity over the conventional CFD methods for computation of inviscid and viscous compressible flows past complex configurations. The main reason for the growth of popularity of these methods is their ability to work on any point distribution. These methods donot require the grid for flow simulation, which is an essential requirement for all other conventional CFD methods. However these methods are limited by the requirement of a good connectivity around a node. Here, a very robust form of the meshfree method called Weighted Least Squares Kinetic Upwind Method using Eigendirections (WLSKUMED) has been used to avoid the problem of code divergence due to the bad connectivity. In WLSKUM-ED, the weights are calculated to diagonalize the least squares matrix A (w) such that the x and y directions become the eigen directions along which the higher dimensional least squares formulae reduce to the corresponding one dimensional formulae. Here an effort has been made to explain the enhanced robustness of the WLSKUM-ED meshfree method over the conventional LSKUM meshfree method. The accuracy of the kinetic meshfree method for the Euler equations has been enhanced by use of entropy variables and inner iterations in the defect correction method. It is observed that the use of entropy variables and inner iterations in the defect correction method helps in obtaining the formasl order of accuracy in case of a non-uniform point distribution.