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Non-equilibrium effects play a vital role in high-speed and rarefied gasflows and the accurate simulation of these flow regimes are far beyond thecapability of near-local-equilibrium Navier-Stokes-Fourier equations. Euproposed generalized hydrodynamic equations which are consistent with the lawsof irreversible thermodynamics to solve this problem. Based on Eu's generalizedhydrodynamics equations, a computational model, namely the nonlinear coupledconstitutive relations(NCCR),was developed by R.S.Myong and appliedsuccessfully to one-dimensional shock wave structure and two-dimensionalrarefied flows. In this paper, finite volume schemes, including LU-SGS timeadvance scheme, MUSCL interpolation and AUSMPW+ scheme, are fistly adopted toinvestigate NCCR model's validity and potential in three-dimensional complexhypersonic rarefied gas flows. Moreover, in order to solve the computationalstability problems in 3D complex flows,a modified solution is developed for theNCCR model. Finally, the modified solution is tested for a slip complex flowover a 3D hollow cylinder-flare configuration. The numerical results show thatthe NCCR model by the modified solution yields good solutions in betteragreement with the DSMC results and experimential data than NSF equations, andimply NCCR model's great potential capability in further application.

A new coupled computational method in conjunction with three-dimensional finite volume schemes for nonlinear coupled constitutive relations