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Semi-implicit characteristic-based boundary treatment for acoustics in low Mach number flows

Abstract : For low Mach number flow calculation, when acoustic waves have to be captured, semi-implicit methods allow to avoid the time-step limitation that arises when explicit schemes are used. A method is suggested to solve the boundary equations so that the semi-implicitness of the algorithm is maintained, as well as its pressure-velocity coupling. This method is studied theoretically and numerically, in the low Mach number regime. Partially non-reflective characteristic-based boundary conditions, with the linear relaxation form suggested by Rudy and Strikwerda, [J. Comput. Phys. 36 (1980) 55-70], are considered. It is shown that their properties, well known in the framework of explicit schemes, are recovered with the proposed semi-implicit treatment and an acoustic CFL number significantly larger than unity.
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Yann Moguen, Erik Dick, Pascal Bruel. Semi-implicit characteristic-based boundary treatment for acoustics in low Mach number flows. Journal of Computational Physics, Elsevier, 2013, 255, pp.339 - 361. ⟨10.1016/j.jcp.2013.08.019⟩. ⟨hal-02359072⟩

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