New developments in kinetic schemes

Abstract

Kinetic schemes for the numerical solution of PDE of fluid dynamics are a new class of upwind schemes. The moment method strategy used in constructing these schemes is based on the connection between the Boltzmann equation of kinetic theory of gases and governing equations of fluid dynamics. Any upwind scheme for the solution of the Boltzmann equation becomes an upwind scheme for the solution of PDE of fluid dynamics by taking suitable moments. This idea has been exploited in the present paper in developing Least Squares Kinetic Upwind Method (LSKUM) and Kinetic Flux vector splitting method on Moving Grid (KFMG). The robustness and versatility of LSKUM has been demonstrated by applying it to 2-D flow problems of inviscid gas dynamics. The LSKUM has been found to operate on any type of grid and can be called a grid fault tolerant scheme in view of the use of least squares approximation to the space derivatives. The KFMG is a promising new method showing how easily the kinetic schemes lend themselves easily to problems involving moving grids which are generally employed while solving problems in unsteady aerodynamics.