一维低马赫反应流的高阶自适应时间离散化：以固体推进剂燃烧为例
High-order adaptive time discretisation of one-dimensional low-Mach reacting flows: a case study of solid propellant combustion
AI总结：
针对一维低马赫反应流求解难题，提出基于刚性精确Runge-Kutta方法的高阶自适应时间离散策略，经固体推进剂燃烧三类算例验证，其效率和精度优于传统方法。
摘要：
采用高阶自适应时间方法求解反应性低马赫Navier-Stokes方程仍是一项具有挑战性的问题，尤其是在处理质量约束中涉及的代数变量方面。我们聚焦于一维构型，这一难题在燃烧学界长期存在。我们研究了一种固体推进剂燃烧模型，该模型具备均质燃烧或喷雾燃烧场景中会遇到的典型难点，还额外存在活动界面带来的复杂性。经空间半离散后得到的系统被证明是指数为1的微分代数系统。我们提出了一种基于刚性精确Runge-Kutta方法的数值策略，对代数约束进行了特殊离散化处理，并引入了时间自适应机制。实验表明，该方法在恰当处理约束的同时，能在所有变量上达到高阶精度。我们研究了三个具有挑战性的测试算例：点火、极限环以及含详细气相动力学的非稳态响应。结果显示，时间积分方法会极大影响系统动力学行为的预测能力。与燃烧文献中使用的传统格式相比，所提出的数值策略在所有算例中均展现出更高的效率和精度。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
