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Pressure-velocity coupling allowing acoustic calculation in low Mach number flow

Abstract : Low Mach number flow computation in co-located grid arrangement requires pressure-velocity coupling in order to prevent the checkerboard phenomenon. Two broad categories of pressure-velocity coupling methods for unsteady flows can be distinguished based on the time-step dependency of the coupling coefficient in the definition of the transporting velocity on a face of a control volume. As an example of the time-step independent category , the AUSM +-up scheme is studied. As an example of the second category, Rhie-Chow momentum interpolation methods are studied. Within the momentum interpolation techniques, again two broad categories can be distinguished based on the time-step dependency of the coupling coefficient used for unsteady flow computations, but when a steady state is reached. Variants of Rhie-Chow interpolation methods in each subcategory are studied on critical test cases. The result of the study is that for a good representation of unsteady flows containing acoustic information, the pressure-velocity coupling coefficient must explicitly depend on the time-step, but that the transporting velocity must become independent of the time-step when a steady state is reached.
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Yann Moguen, Tarik Kousksou, Pascal Bruel, Jan Vierendeels, Erik Dick. Pressure-velocity coupling allowing acoustic calculation in low Mach number flow. Journal of Computational Physics, Elsevier, 2012, 231 (16), pp.5522-5541. ⟨10.1016/j.jcp.2012.05.001⟩. ⟨hal-02358963⟩

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