Unsteady counterflows are employed to understand and model the effect of turbulence on flames. We present a novel numerical approach for the simulation of one-dimensional unsteady counterflow flames with fourth order spatial discretization and up to fourth order time discretization. The approach couples a three-stage Lobatto IIIa formula for boundary value problems and variable-order, variable time step size Backward Differentiation Formulas for time integration. The framework is explained in detail, its computational performance is analysed, and its use is demonstrated for the case of stochastic forcing of premixed counterflow flames, whereby the imposed rate of strain is a multi-scale lognormal discrete random process with exponential autocorrelation. High-order spatial and temporal discretization make the approach well-suited for the accurate and computationally efficient simulation of the effect of turbulence on flames, which are characterised by large amplitude stochastic fluctuations of the local rate of strain.

采用不稳定逆流来理解和模拟湍流对火焰的影响。我们提出了一种新颖的数值方法，用于模拟具有四阶空间离散和高达四阶时间离散的一维非定常逆流火焰。该方法结合了用于边值问题的三阶段 Lobatto IIIa 公式和用于时间积分的变阶、可变时间步长后向微分公式。详细解释了该框架，分析了其计算性能，并演示了其在预混合逆流火焰随机强迫情况下的使用，其中施加的应变率是具有指数自相关的多尺度对数正态离散随机过程。