An Undecomposed Hybrid Algorithm for Nonlinear Coupled Constitutive Relations of Rarefied Gas Dynamics (Communications in Computational Physics, 2019)
It is well-established that the accurate simulation of hypersonic rarefied gasflows cannot be accomplished by Navier-Stokes-Fourier (NSF) equations since theyare applicable only for small deviations from local thermodynamic equilibrium. To accurately and efficiently solve this problem, a nonlinear-coupled-constitutive-relation(NCCR) model was developed from Eu's generalized hydrodynamic equations, whichare consistent with the laws of irreversible thermodynamics. In this paper, Myong'sdecomposed solver is extended for solving three-dimensional diatomic nonlinear coupled algebraic constitutive equations. Subsequently, a reliable undecomposed hybridalgorithm is proposed for the complete solution of NCCR model through combiningthe merits of fixed-point and Newton's iterations. The new-developed computationalmethod is validated by high-speed rarefied flows around a cylinder and the Apollocommand module. Computation shows that the undecomposed hybrid algorithmmakes a great improvement in computational robustness and accuracy. Moreover, thisnonlinear constitutive model yields solutions in better agreement with DSMC thanNSF model. The results indicate that NCCR model is capable of capturing the physicalflow properties away from equilibrium and demonstrate its great potential capabilityin the further application.