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In this paper, we extend the unified gas-kinetic wave-particle (UGKWP) methodto the multi-species gas mixture and multiscale plasma transport. Theconstruction of the scheme is based on the direct modeling on the mesh size andtime step scales, and the local cell's Knudsen number determines the flowphysics. The proposed scheme has the multiscale and asymptotic complexitydiminishing properties. The multiscale property means that according to cell'sKnudsen number the scheme can capture the non-equilibrium flow physics in therarefied flow regime, and preserve the asymptotic Euler, Navier-Stokes, andmagnetohydrodynamics limit in the continuum regime. The asymptotic complexitydiminishing property means that the total degree of freedom of the schemeautomatically decreases as cell's Knudsen number decreases. In the continuumregime, the scheme automatically degenerates from a kinetic solver to ahydrodynamic solver. In UGKWP, the evolution of microscopic velocitydistribution is coupled with the evolution of macroscopic variables, and theparticle evolution as well as the macroscopic fluxes are modeled from the timeaccumulating solution up to a time step scale from the kinetic model equation.  For plasma transport, current scheme provides a smooth transition fromparticle in cell (PIC) method in the rarefied regime to the magnetohydrodynamic(MHD) solver in the continuum regime. In the continuum limit, the cell size andtime step of the UGKWP method is not restricted to be less than the mean freepath and mean collision time. In the highly magnetized regime, the cell sizeand time step are not restricted by the Debye length and plasma cyclotronperiod. The multiscale and asymptotic complexity diminishing properties of thescheme are verified by numerical tests in multiple flow regimes.

Unified Gas-kinetic Wave-Particle Method IV: Multi-species Gas Mixture and Plasma Transport