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For increasingly rarefied flowfields, the Navier-Stokes (NS) equations loseaccuracy partially due to the single temperature approximation. To overcomethis barrier, a continuum multi-temperature model based on theBhatnagar-Gross-Krook (BGK) equation coupled with the Landau-Teller-Jeansrelaxation model has been proposed for two-dimensional hypersonicnon-equilibrium multi-temperature flow computation. In recent study, atwo-stage fourth-order gas-kinetic scheme (GKS) has been developed forequilibrium flows, which achieves a fourth-order accuracy in space and time aswell as high efficiency and robustness. In this paper, targeting for accurateand efficient simulation of multi-temperature non-equilibrium flows, ahigh-order three-dimensional multi-temperature GKS is implemented under thetwo-stage fourth-order framework, with the fourth-order Simpson interpolationrule for the newly emerged source term. Simulations on decaying homogeneousisotropic turbulence, low-density nozzle flow, rarefied hypersonic flow over aflat plate, and type IV shock-shock interaction are used to validate themulti-temperature model through the comparison with experimental measurements.The unified gas kinetic scheme (UGKS) results, and the Direct simulation MonteCarlo (DSMC) solutions will be used as well in some cases for validation.Computational results not only confirm the high-order accuracy and quiterobustness of this scheme, but also show the significant improvement oncomputational efficiency compared with UGKS and DSMC, especially in the nearcontinuum flow regime.

Physical Modeling and Numerical Studies of Three-dimensional Non-equilibrium Multi-temperature Flows