Numerical methods for model kinetic equations and their application to external high-speed flows - Vladimir Titarev (Federal Research Center "Computer Science and control", Russian Academy of Sciences, Russia)

Abstract:

During last ten years the author has been developing a discrete-velocity-type numerical method to solve model kinetic equation with the E.M. Shakhov collision integral for three-dimensional flows.  The method combines a high-order TVD advection scheme  for arbitrary spatial meshes, unstructured mesh in velocity space with adaptation for high-speed flows and one-step LU-SGS implicit time evolution method. These features allow applications to industrial-type problems with complex geometries. This presentation is a review of all recent developments of this numerical method for high-speed flows, which have been carried out by the author alone or with the collaborators from the Russian academy of Sciences. These developments primarily concern various studies of the stationary high-speed flows up to free-stream Mach number M=25 as well as comparison of kinetic and direct simulation Monte-Carlo (DSMC) solutions. Possible extension to diatomic gases will also be discussed.