化学非平衡流动解耦算法的回顾与新进展

超声速化学非平衡流动的数值模拟一直是计算流体力学领域的难点，主要体现在如下几个方面：物理过程非常复杂，存在着激波、燃烧波等各种复杂波系的相互作用；超声速化学非平衡流动属于典型的时空多尺度物理问题，其控制方程存在严重的刚性，给数值求解带来了很大困难。对国内外的解耦算法研究现状简单综述后，主要介绍1993年刘君提出的解耦算法的理论基础，流动方程采用冻结流模型，源项方程模拟流体微团在当地绝热、定容的热力学系统内发生的化学反应过程。通过引入两个中间变量，即等效内能和等效比热比，将与温度无关的生成焓从流动方程组能量项中分离出去，源项方程组中包含等效内能，使用不同算子对流动方程和源项方程解耦求解。与传统解耦算法相比，源项方程的求解过程中包含状态参数和组元同时变化。结合刘君解耦算法机理和有限体积法空间平均特性，介绍近期在提高算法计算效率方面的研究进展，包括流动方程优化算法和耦合过程优化。采用优化算法对经典的激波诱导燃烧算例进行数值模拟，与不同文献结果进行对比，验证了优化算法的时空精度。通过总结经验发现化学非平衡反应仅发生在流场局部区域，提出质量生成率判据，结合相应模拟结果验证了方法的可行性，可以进一步提高化学反应算子的计算效率。

Review and recent advances in uncoupled algorithms for chemical non-equilibrium flows

Numerical simulation of supersonic chemical non-equilibrium flow is a challenge in computational fluid dynamics because of two main reasons. First, the physical process is very complex because many interactions occur between shock waves and other intricate phenomena. Second, the supersonic chemical non-equilibrium flow is a typical space-time multi-scale physical problem, and its governing equations can result in serious rigidity to significantly affect numerical simulation. This paper concentrates on an introduction of Liu's uncoupled methods for simulating chemical non-equilibrium flow, following a brief review of the development home and abroad. In Liu's method, the flow equations use frozen flow model, and the reaction source equations simulate chemical reaction process in the local adiabatic and constant volume thermodynamic system. The temperature-independent enthalpy is separated from the energy term by introducing the equivalent internal energy and equivalent specific heat ratio. The flow and source equations are solved using different operators. Different from classical uncoupled methods, the solution for source term equation includes simultaneous change of state parameters and components. Considering Liu's uncoupled method and the space mean characteristic of the finite volume method, this paper also introduces recent advances in improving computational efficiency, including the flow equation optimization method and the optimization of the coupling process. Numerical simulation of shock-induced combustion is conducted using the optimization method, and the accuracy of the method is verified by comparing the results with those in literature. The chemical non-equilibrium reaction is found to occur only locally. According to the mass production rate criterion, the feasibility of the method is verified using the corresponding simulation results, and the computational efficiency of the chemical reaction operator can be improved.