Simplified hydrodynamic-wave particle method for the multiscale rarefied flow

Abstract

Coupling the Computational Fluid Dynamics (CFD) with the stochastic particle method to address multi-scale rarefied flows remains of great interest to many researchers. Rather than involving the field decomposition and the information exchange, the simplified hydrodynamic-wave particle method (SHWPM) has been proposed in this paper to automatically switch from the stochastic particle solver to the conventional CFD method in the multi-scale simulation. The weights to couple the respective numerical fluxes are derived based on the integral solution of the Boltzmann equation. By introducing the simplified hydrodynamic-wave flux that can be computed by the linear combination of inviscid and viscous fluxes from the conventional CFD solver, the collision effects of particles are calculated in a macroscopic approach and the number of sampling particles could be significantly reduced in the near-continuum regime. Error analysis demonstrates that the simplified treatment can preserve the second-order accuracy and asymptotic preserving property of the present method in both the continuum and free molecular limits. Several numerical cases over a wide range of Knudsen and Mach numbers exhibit the capability of SHWPM for modeling the multiscale flow accurately and efficiently. The example of hypersonic flow passing a cylinder shows that the SHWPM could achieve tens of times speedup ratio compared to the discrete velocity method (DVM) in the continuum regime.