  For increasingly rarefied flowfields, the Navier-Stokes (NS) equations lose
accuracy partially due to the single temperature approximation. To overcome
this barrier, a continuum multi-temperature model based on the
Bhatnagar-Gross-Krook (BGK) equation coupled with the Landau-Teller-Jeans
relaxation model has been proposed for two-dimensional hypersonic
non-equilibrium multi-temperature flow computation. In recent study, a
two-stage fourth-order gas-kinetic scheme (GKS) has been developed for
equilibrium flows, which achieves a fourth-order accuracy in space and time as
well as high efficiency and robustness. In this paper, targeting for accurate
and efficient simulation of multi-temperature non-equilibrium flows, a
high-order three-dimensional multi-temperature GKS is implemented under the
two-stage fourth-order framework, with the fourth-order Simpson interpolation
rule for the newly emerged source term. Simulations on decaying homogeneous
isotropic turbulence, low-density nozzle flow, rarefied hypersonic flow over a
flat plate, and type IV shock-shock interaction are used to validate the
multi-temperature model through the comparison with experimental measurements.
The unified gas kinetic scheme (UGKS) results, and the Direct simulation Monte
Carlo (DSMC) solutions will be used as well in some cases for validation.
Computational results not only confirm the high-order accuracy and quite
robustness of this scheme, but also show the significant improvement on
computational efficiency compared with UGKS and DSMC, especially in the near
continuum flow regime.
