全隐LU-SGS算法在高超声速热化学非平衡流刚性问题中的应用

在高超声速热化学非平衡流动计算中，当地气体能量松弛时间、化学反应特征时间与流动时间推进步长量级差异过大会带来严重数值刚性问题，且在高雷诺数条件下，壁面、拐角等强干扰区网格加密使得该问题加剧，导致初始最大CFL数极小，收敛速度缓慢。原始LU-SGS算法仅考虑化学反应源项和对流项的隐式处理，通过推导黏性项Jacobian矩阵谱半径并采用对角近似处理，发展了热化学非平衡FLU-SGS和BLU-SGS两种全隐LU-SGS算法；针对高焓二维圆柱和轴对称返回舱算例，对比改进前后三种算法的收敛特性。结果表明，FLU-SGS及BLU-SGS算法能够快速建立强黏性干扰和大分离流场、解决热化学非平衡复杂流计算中的刚性问题，实现初始最大CFL数3至5个量级的提升，加速收敛效果明显。

Fully implicit LU-SGS algorithms applied to stiff problems in hypersonic thermochemical non-equilibrium flows

In hypersonic thermochemical nonequilibrium flow calculations, a large difference between the numerical time step and the molecular vibration relaxation time or the chemical reaction time can bring about serious numerical stiffness problems, which are exacerbated by grid refinement in strong interaction areas such as near-wall or corner. The initial maximum CFL number and convergence rate are thus limited under high Reynolds conditions. The original LU-SGS algorithm only considers the implicit treatment of the source term and convection term. Two fully implicit LU-SGS algorithms, the FLU-SGS algorithm and the BLU-SGS algorithm, were developed by deriving and implementing the diagonal approximation of the spectral radius of the viscous Jacobian matrix. The convergence speeds of the three algorithms were investigated in cases of high enthalpy two-dimensional cylinder flow and axisymmetric re-entry capsule flow. The results show that strong viscous interaction and large separation can be quickly established and 3~5 orders of increase of the maximum CFL number can be reached with FLU-SGS and BLU-SGS algorithms. Thus the newly developed algorithms are efficient in accelerating convergence in the calculation of complex thermochemical non-equilibrium flows.