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Volume 8, Issue 6
Stability Analysis of a Fully Coupled Implicit Scheme for Inviscid Chemical Non-Equilibrium Flows

Yu Wang, Jinsheng Cai & Kun Qu

Adv. Appl. Math. Mech., 8 (2016), pp. 953-970.

Published online: 2018-05

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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.

  • AMS Subject Headings

65M12, 65F10, 76K05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-8-953, author = {Wang , YuCai , Jinsheng and Qu , Kun}, title = {Stability Analysis of a Fully Coupled Implicit Scheme for Inviscid Chemical Non-Equilibrium Flows}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {6}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2015.m1043}, url = {http://global-sci.org/intro/article_detail/aamm/12125.html} }
TY - JOUR T1 - Stability Analysis of a Fully Coupled Implicit Scheme for Inviscid Chemical Non-Equilibrium Flows AU - Wang , Yu AU - Cai , Jinsheng AU - Qu , Kun JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 953 EP - 970 PY - 2018 DA - 2018/05 SN - 8 DO - http://doi.org/10.4208/aamm.2015.m1043 UR - https://global-sci.org/intro/article_detail/aamm/12125.html KW - Stability, LU-SGS, non-equilibrium flows, Euler equations, flux Jacobian, grid refinement. AB -

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.

Yu Wang, Jinsheng Cai & Kun Qu. (2020). Stability Analysis of a Fully Coupled Implicit Scheme for Inviscid Chemical Non-Equilibrium Flows. Advances in Applied Mathematics and Mechanics. 8 (6). 953-970. doi:10.4208/aamm.2015.m1043
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