We present an efficient, accurate computational method for a coordinate-free model of flame front propagation of Frankel and Sivashinsky. This model allows for overturned flames fronts, in contrast to weakly nonlinear models such as the Kuramoto–Sivashinsky equation. The numerical procedure adapts the method of Hou, Lowengrub and Shelley, derived for vortex sheets, to this model. The result is a nonstiff, highly accurate solver which can handle fully nonlinear, overturned interfaces, with similar computational expense to methods for weakly nonlinear models. We apply this solver both to simulate overturned flame fronts and to compare the accuracy of Kuramoto–Sivashinsky and coordinate-free models in the appropriate limit.

中文翻译：

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火焰前沿无坐标模型的有效计算

我们为弗兰克尔和西瓦辛斯基的火焰前沿传播的无坐标模型提出了一种有效、准确的计算方法。与 Kuramoto-Sivashinsky 方程等弱非线性模型相比，该模型允许翻转火焰前沿。数值程序采用了从涡片推导出来的侯、洛文格鲁布和雪莱的方法，适用于该模型。结果是一个非刚性、高精度的求解器，它可以处理完全非线性、翻转的界面，其计算成本与弱非线性模型的方法相似。我们应用这个求解器来模拟翻转的火焰前锋，并比较 Kuramoto-Sivashinsky 和无坐标模型在适当限制下的精度。