Adaptive wave-particle decomposition in UGKWP method for high-speed flow simulations

Abstract

With wave-particle decomposition, a unified gas-kinetic wave-particle (UGKWP) method has been developed for multiscale flow simulations. With the variation of the cell Knudsen number, the UGKWP method captures the transport process in all flow regimes without the kinetic solver’s constraint on the numerical mesh size and time step being determined by the kinetic particle mean free path and particle collision time. In the current UGKWP method, the cell Knudsen number, which is defined as the ratio of particle collision time to numerical time step, is used to distribute the components in the wave-particle decomposition. The adaptation of particles in the UGKWP method is mainly for the capturing of the non-equilibrium transport. In this aspect, the cell Knudsen number alone is not enough to identify the non-equilibrium state. For example, in the equilibrium flow regime with a Maxwellian distribution function, even at a large cell Knudsen number, the flow evolution can be still modelled by the Navier-Stokes solver. More specifically, in the near space environment both the hypersonic flow around a space vehicle and the plume flow from a satellite nozzle will encounter a far field rarefied equilibrium flow in a large computational domain. In the background dilute equilibrium region, the large particle collision time and a uniform small numerical time step can result in a large local cell Knudsen number and make the UGKWP method track a huge number of particles for the far field background flow in the original approach. But, in this region the analytical wave representation can be legitimately used in the UGKWP method to capture the nearly equilibrium flow evolution. Therefore, to further improve the efficiency of the UGKWP method for multiscale flow simulations, an adaptive UGKWP (AUGKWP) method is developed with the introduction of an additional local flow variable gradient-dependent Knudsen number. As a result, the wave-particle decomposition in the UGKWP method is determined by both the cell and gradient Knudsen numbers, and the use of particles in the UGKWP method is solely to capture the non-equilibrium flow transport. The current AUGKWP method becomes much more efficient than the previous one with the cell Knudsen number only in the determination of wave-particle composition. Many numerical tests, including Sod shock tube, normal shock structure, hypersonic flow around cylinder, flow around reentry capsule, and an unsteady nozzle plume flow, have been conducted to validate the accuracy and efficiency of the AUGKWP method. Compared with the original UGKWP method, the AUGKWP method achieves the same accuracy, but has advantages in memory reduction and computational efficiency in the simulation for flows with the co-existing of multiple regimes.