Unified gas-kinetic wave-particle methods. II. Multiscale simulation on unstructured mesh

Abstract

In this paper, we present a unified gas-kinetic wave-particle (UGKWP) method on unstructured mesh for the multiscale simulation of continuum and rarefied flow. Inheriting from the multiscale transport in the unified gas-kinetic scheme (UGKS), the integral solution of the kinetic model equation is employed in the construction of the UGKWP method to model the flow physics on the scales of cell size and time step. A novel wave-particle adaptive formulation is introduced in the UGKWP method to describe the flow dynamics in each control volume. The local gas evolution is constructed through the dynamical interaction of the deterministic hydrodynamic wave and the stochastic kinetic particle. To model the gas dynamics on the scales of cell size and time step, the decomposition, interaction, and evolution of the hydrodynamic wave and the kinetic particle depend on the ratio of time step to local collision time. In the rarefied flow regime, the UGKWP method recovers the nonequilibrium flow physics by discrete particles and performs as a stochastic particle method. In the continuum flow regime, the UGKWP method captures the flow behavior solely by macroscopic variable evolution and becomes a gas-kinetic hydrodynamic flow solver, the same as the gas-kinetic scheme, for viscous and heat-conducting Navier–Stokes solutions. In the transition regime, both kinetic particle and hydrodynamic wave contribute adaptively in the UGKWP to capture the peculiar nonequilibrium flow physics in a most efficient way. In different flow regimes, the Sod shock tube, lid-driven cavity flow, laminar boundary layer, and high-speed flow around a circular cylinder are computed to validate the UGKWP method on unstructured mesh. The UGKWP method obtains the same UGKS solutions in all Knudsen regimes. However, with an automatic wave-particle decomposition, the UGKWP method becomes very efficient. For example, at Mach number 30 and Knudsen number 0.1, the UGKWP has several-order-of-magnitude reductions in computational cost and memory requirement in comparison with UGKS. Overall, the UGKWP can capture the gas dynamics in all flow regimes efficiently and accurately from the free molecular transport to the Navier-Stokes flow evolution.