一种用于多组分反应流模拟的组分分裂隐式时间积分方法
A component-splitting implicit time integration for multicomponent reacting flows simulations
AI总结：
针对多组分反应流隐式积分收敛慢、成本高的问题，提出组分分裂隐式方法，结合一致性修正保证精度，经数值验证可有效加速收敛且效率随组分数和CFL数提升而增强。
摘要：
本文提出一种组分分裂方法，用于改善可压缩多组分反应流隐式时间积分的收敛特性。多组分Navier-Stokes方程通量雅可比矩阵的特征分解会产生大型稀疏特征系统，给隐式方法带来收敛慢、计算成本高的挑战。为解决该问题，组分分裂方法将隐式算子拆分为两部分：一部分对应流动方程（密度/动量/能量），另一部分对应组分方程。两部分的隐式算子均基于各自的谱半径采用通量矢量分裂，以实现收敛加速。该方法提升了隐式迭代的计算效率，缓解了时间成本随组分数呈二次增长的问题。本文提出两种一致性修正方法，以降低引入的组分分裂误差并保证质量分数的数值一致性。重要的是，当残差趋近收敛时，组分分裂方法对精度的影响极小。本文通过多个涉及热化学非平衡高超声速流的数值算例，深入研究了组分分裂方法的精度、效率与鲁棒性，并与耦合隐式格式进行对比。结果表明，组分分裂方法减少了残差和壁面热流收敛所需的迭代步数，降低了单步迭代的计算时间，且能将残差降至更低的量级。其加速效率随CFL数和组分数的增加而提升。
英文摘要：
A component-splitting method is proposed to improve convergence characteristics for implicit time integration of compressible multicomponent reactive flows. The characteristic decomposition of flux jacobian of multicomponent Navier-Stokes equations yields a large sparse eigensystem, presenting challenges of slow convergence and high computational costs for implicit methods. To addresses this issue, the component-splitting method segregates the implicit operator into two parts: one for the flow equations (density/momentum/energy) and the other for the component equations. Each part's implicit operator employs flux-vector splitting based on their respective spectral radii to achieve accelerated convergence. This approach improves the computational efficiency of implicit iteration, mitigating the quadratic increase in time cost with the number of species. Two consistence corrections are developed to reduce the introduced component-splitting error and ensure the numerical consistency of mass fraction. Importantly, the impact of component-splitting method on accuracy is minimal as the residual approaches convergence. The accuracy, efficiency, and robustness of component-splitting method are thoroughly investigated and compared with the coupled implicit scheme through several numerical cases involving thermo-chemical nonequilibrium hypersonic flows. The results demonstrate that the component-splitting method decreases the required number of iteration steps for convergence of residual and wall heat flux, decreases the computation time per iteration step, and diminishes the residual to lower magnitude. The acceleration efficiency is enhanced with increases in CFL number and number of species.
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