Adaptive Moving Finite Element Method for Steady Low-Mach-Number Compressible Combustion Problems

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The main contribution of this work is to present the theoretical and practical aspects of the mesh adaptivity, with an emphasis on simulating a reactive flow in a low-Mach-number case. The design of adaptive mesh considered here for solving physical PDEs is characterized by a grid where the mesh nodes move continuously in time while adapting to the evolution of the features of the numerical solutions described in the monitor function that is prescribed by the user. To capture the characteristics of the flame structure when using detailed chemistry, a much more stringent requirement on the spatial resolution of some intermediate species is necessary; thus, the design of an economical and effective mesh also becomes a challenging task.