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 - <p style="text-align: justify;">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.</p>