  In this paper, the unified gas-kinetic wave-particle (UGKWP) method is
further developed for diatomic gas with the energy exchange between
translational and rotational modes for flow study in all regimes. The
multiscale transport mechanism in UGKWP is coming from the direct modeling in a
discretized space, where the cell's Knudsen number, defined by the ratio of
particle mean free path over the numerical cell size, determines the flow
physics simulated by the wave particle formulation. The non-equilibrium
distribution function in UGKWP is tracked by the discrete particle and
analytical wave. The weights of distributed particle and wave in different
regimes are controlled by the accumulating evolution solution of particle
transport and collision within a time step, where distinguishable macroscopic
flow variables of particle and wave are updated inside each control volume.
With the variation of local cell's Knudsen number, the UGKWP becomes a particle
method in the highly rarefied flow regime and converges to the gas-kinetic
scheme (GKS) for the Navier-Stokes solution in the continuum flow regime
without particles. Even targeting on the same solution as the discrete velocity
method (DVM)-based unified gas-kinetic scheme (UGKS), the computational cost
and memory requirement in UGKWP could be reduced by several orders of magnitude
for the high speed and high temperature flow simulation, where the
translational and rotational non-equilibrium becomes important in the
transition and rarefied regime. As a result, 3D hypersonic computations around
a flying vehicle in all regimes can be conducted using a personal computer. The
UGKWP method for diatomic gas will be validated in various cases from one
dimensional shock structure to three dimensional flow over a sphere, and the
numerical solutions will be compared with the reference DSMC results and
experimental measurements.
