A Hybrid Adaptive Low-Mach-Number/Compressible Method for the Euler Equations

This paper presents a novel hybrid method for solving the low-Mach-number equations for inviscid flow supplemented with long wavelength acoustics as computed by solving the fully compressible Euler equations. Contrary to previous existing methods, the novelty of the present strategy is that the fully compressible equations are solved without any approximation, and that an adaptive mesh refinement (AMR) framework is employed to optimize the performance of the algorithm. It is demonstrated that compared to a purely compressible approach, the hybrid method allows time-steps of larger magnitude at the finest level, leading to an overall reduction of the computational time.