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Stability Analysis of a Fully Coupled Implicit Scheme for Inviscid Chemical Non-Equilibrium Flows

Part of: Numerical linear algebra Partial differential equations, initial value and time-dependent initial-boundary value problems Hypersonic flows

Published online by Cambridge University Press:  19 September 2016

Yu Wang ,
Jinsheng Cai  and
Kun Qu
Yu Wang*
Affiliation:
National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an 710072, China
Jinsheng Cai*
Affiliation:
National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an 710072, China
Kun Qu*
Affiliation:
National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an 710072, China
*
*Corresponding author. Email:wangyu@mail.nwpu.edu.cn (Y.Wang), kunqu@nwpu.edu.cn (K. Qu), caijsh@nwpu.edu.cn (J. S. Cai)
*Corresponding author. Email:wangyu@mail.nwpu.edu.cn (Y.Wang), kunqu@nwpu.edu.cn (K. Qu), caijsh@nwpu.edu.cn (J. S. Cai)
*Corresponding author. Email:wangyu@mail.nwpu.edu.cn (Y.Wang), kunqu@nwpu.edu.cn (K. Qu), caijsh@nwpu.edu.cn (J. S. Cai)
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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.

Keywords

StabilityLU-SGSnon-equilibrium flowsEuler equationsflux Jacobiangrid refinement

MSC classification

Secondary: 65M12: Stability and convergence of numerical methods 65F10: Iterative methods for linear systems 76K05: Hypersonic flows
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 6 , December 2016 , pp. 953 - 970
Copyright
Copyright © Global-Science Press 2016 

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