Year: 2016
Author: Yu Wang, Jinsheng Cai, Kun Qu
Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 6 : pp. 953–970
Abstract
Von Neumann stability theory is applied to analyze the stability of a fully coupled implicit (FCI) scheme based on the lower-upper symmetric Gauss-Seidel (LU-SGS) method for inviscid chemical non-equilibrium flows. The FCI scheme shows excellent stability except the case of the flows involving strong recombination reactions, and can weaken or even eliminate the instability resulting from the stiffness problem, which occurs in the subsonic high-temperature region of the hypersonic flow field. In addition, when the full Jacobian of chemical source term is diagonalized, the stability of the FCI scheme relies heavily on the flow conditions. Especially in the case of high temperature and subsonic state, the CFL number satisfying the stability is very small. Moreover, we also consider the effect of the space step, and demonstrate that the stability of the FCI scheme with the diagonalized Jacobian can be improved by reducing the space step. Therefore, we propose an improved method on the grid distribution according to the flow conditions. Numerical tests validate sufficiently the foregoing analyses. Based on the improved grid, the CFL number can be quickly ramped up to large values for convergence acceleration.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2015.m1043
Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 6 : pp. 953–970
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Stability LU-SGS non-equilibrium flows Euler equations flux Jacobian grid refinement.
Author Details
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A spectral radius scaling semi-implicit iterative time stepping method for reactive flow simulations with detailed chemistry
Xie, Qing
Xiao, Zhixiang
Ren, Zhuyin
Journal of Computational Physics, Vol. 368 (2018), Iss. P.47
https://doi.org/10.1016/j.jcp.2018.04.042 [Citations: 11]