论文标题
一维低操作反应流的高阶自适应时间离散：固体推进剂燃烧的案例研究
High-order adaptive time discretisation of one-dimensional low-Mach reacting flows: a case study of solid propellant combustion
论文作者
论文摘要
在时间上求解具有高阶自适应方法的反应性低实纳维尔 - 斯托克斯方程仍然是一个具有挑战性的问题，尤其是由于处理质量约束所涉及的代数变量。我们专注于一维配置，在燃烧社区中长期存在这一挑战。我们考虑了一种固体推进剂燃烧模型，该模型具有在均匀或喷雾燃烧案例中遇到的特征困难，并增加了活动界面的并发症。在空间中半差异后获得的系统显示为索引1的差异代数。引入了依赖于僵化精确的runge-kutta方法的数值策略，并具有代数约束和时间适应的特定离散化。高阶显示在所有变量上可以达到所有变量，同时正确处理约束。研究了三个具有挑战性的测试用例：点火，限制周期和不稳定的响应，并具有详细的气相动力学。我们表明，时间集成方法可以极大地影响预测系统动力学的能力。与燃烧文献中使用的传统方案相比，提出的数值策略在所有情况下均表现出很高的效率和准确性。
Solving the reactive low-Mach Navier-Stokes equations with high-order adaptive methods in time is still a challenging problem, in particular due to the handling of the algebraic variables involved in the mass constraint. We focus on the one-dimensional configuration, where this challenge has long existed in the combustion community. We consider a model of solid propellant combustion, which possesses the characteristic difficulties encountered in the homogeneous or spray combustion cases, with the added complication of an active interface. The system obtained after semi-discretisation in space is shown to be differential-algebraic of index 1. A numerical strategy relying on stiffly accurate Runge-Kutta methods is introduced, with a specific discretisation of the algebraic constraints and time adaptation. High order is shown to be reached on all variables, while handling the constraints properly. Three challenging test cases are investigated: ignition, limit cycle, and unsteady response with detailed gas-phase kinetics. We show that the time integration method can greatly affect the ability to predict the dynamics of the system. The proposed numerical strategy exhibits high efficiency and accuracy for all cases compared to traditional schemes used in the combustion literature.
