A new high-order multidimensional scheme

Abstract

A third-order accurate multidimensional gas-kinetic BGK scheme is constructed through the high-order expansion of the distribution function and the high-order reconstruction of conservative variables. With several typical test cases the good performance of the new scheme is validated in both smooth flow and the flow with strong discontinuity. The theoretical validity for such an approach is due to the fact that the kinetic equation has no specific requirement on the smoothness of the initial data, as well as the simple particle transport mechanism and the inherent multidimensional characteristics on the microscopic level. The present study shows a new hierarchy to construct a high-order multidimensional method, and the Navier-Stokes flux function obtained from the present work can be adapted to many other high-order CFD methods. © 2011 Springer-Verlag Berlin Heidelberg.