A computational strategy for nonlinear coupled constitutive relations of rarefied nonequilibrium flows on unstructured grids

Abstract

The Navier-Stokes-Fourier (NSF) equations are no longer valid in high-Knudsen and high-Mach flows, where the local thermodynamically equilibrium assumption fails, while the nonlinear coupled constitutive relations (NCCR) have been proven to be an efficient approach for rarefied non-equilibrium flows under the structured finite-volume-method computational fluid dynamic (FVM-CFD) solver. In this paper, by adding the time derivatives of non-conserved variables to the NCCR model, a computational strategy for NCCR model under the unstructured FVM-CFD framework is first proposed for further engineering applications. An upwind flux-splitting scheme with the Lower-Upper Symmetric Gauss-Seidel (LU-SGS) implicit time-marching scheme is employed. The linear stability of one-dimensional modified NCCR model in time and space is analyzed subsequently, which indicates the modified NCCR model is unconditionally stable. The accuracy and computational performance of the proposed NCCR solution are assessed by a feat of the numerical tests for hypersonic flow over a blunt cylinder without a wake, supersonic flow past a circular cylinder with a wake, and hypersonic flow around a planetary probe. Computational results show that the newly-developed NCCR solution can get solutions in better agreement with the direct simulation Monte Carlo (DSMC) than NSF results. Moreover, the newly-developed NCCR solution has a better property of convergence than the undecomposed NCCR algorithm under the unstructured FVM-CFD framework. These superior advantages of the present computational strategy are expected to make the NCCR method a promising engineering tool for modeling rarefied non-equilibrium flows.