Unified gas-kinetic wave-particle methods IV: multi-species gas mixture and plasma transport

Chang Liu,Kun Xu

doi:10.1186/s42774-021-00062-1

Abstract

In this paper, we extend the unified gas-kinetic wave-particle (UGKWP) methods to the multi-species gas mixture and multiscale plasma transport. The construction of the scheme is based on the direct modeling on the mesh size and time step scales, and the local cell’s Knudsen number determines the flow physics. The proposed scheme has the multiscale and asymptotic complexity diminishing properties. The multiscale property means that according to the cell’s Knudsen number the scheme can capture the non-equilibrium flow physics when the cell size is on the kinetic mean free path scale, and preserve the asymptotic Euler, Navier-Stokes, and magnetohydrodynamics (MHD) when the cell size is on the hydrodynamic scale and is much larger than the particle mean free path. The asymptotic complexity diminishing property means that the total degrees of freedom of the scheme reduce automatically with the decreasing of the cell’s Knudsen number. In the continuum regime, the scheme automatically degenerates from a kinetic solver to a hydrodynamic solver. In the UGKWP, the evolution of microscopic velocity distribution is coupled with the evolution of macroscopic variables, and the particle evolution as well as the macroscopic fluxes is modeled from a time accumulating solution of kinetic scale particle transport and collision up to a time step scale. For plasma transport, the current scheme provides a smooth transition from particle-in-cell (PIC) method in the rarefied regime to the magnetohydrodynamic solver in the continuum regime. In the continuum limit, the cell size and time step of the UGKWP method are not restricted by the particle mean free path and mean collision time. In the highly magnetized regime, the cell size and time step are not restricted by the Debye length and plasma cyclotron period. The multiscale and asymptotic complexity diminishing properties of the scheme are verified by numerical tests in multiple flow regimes.

Highlights

Gas mixture and plasma widely exit in the universe and are extensively applied in the industry of aerospace, chemical, and nuclear engineering
We show that the unified gas-kinetic wave-particle (UGKWP) method is a second order UP scheme and an asymptotic complexity diminishing scheme
The construction of numerical scheme for multiscale transport is based on the direct modeling methodology [23], where the flow physics is modeled on the cell size and time step scales

Summary

Introduction

Gas mixture and plasma widely exit in the universe and are extensively applied in the industry of aerospace, chemical, and nuclear engineering. In the highly magnetized flow regime where the normalized Larmor radius approaches zero and Debye length is on the order of the reciprocal of the speed of light, a single fluid ideal MHD can be used to describe the large scale plasma physics [8]. For both multiscale gas mixture and plasma transport, the hydrodynamic descriptions are more effective, but limited in the continuum flow regime; while the kinetic models capture kinetic scale physics, but have complex form and high dimensionality. In order to capture flow physics in different regimes in a corresponding most efficient way, the construction of multiscale method for gas mixture and plasma transport is highly demanded

Objectives

Discussion

Conclusion