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

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.