Assessment of the cubic Fokker-Planck-DSMC hybrid method for hypersonic rarefied flows past a cylinder

Abstract

Hypersonic vehicles experience a wide range of Knudsen number regimes due to changes in atmospheric density. The Direct Simulation Monte Carlo (DSMC) method is physically accurate for all flow regimes, however it is relatively computationally expensive in high density, and low Knudsen number regions. Recent advances in the Fokker-Planck (FP) kinetic models have addressed this issue by approximating the particle collisions involved in the Boltzmann collision integral with continuous stochastic processes. Furthermore, a coupled FP-DSMC solution method has been devised aiming at a universally effic ient yet accurate solution algorithm for rarefied gas flows. Well known Lofthouse case of a generic hypersonic flow about a cylinder (Mach 10, Kn 0.01, Argon) is selected to investigate the performance of a hybrid FP-DSMC implementation. The effect of molecular potential on the accuracy of the scheme is mainly analyzed. Furthermore, spatial resolution of cubic FP scheme is studied. Finally, detailed study of accuracy and efficiency of FP-DSMC hybrid scheme is discussed. It is found that the presented adaptive grid together with the FP-DSMC method results in a factor of six speed up for considered hypersonic flow about a cylinder.