a b s t r a c tLow Mach number flow computation in co-located grid arrangement requires pressurevelocity 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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An active inline mixer suitable for flows at low Reynolds number and high Péclet number is studied. An alternated oscillatory forcing protocol is imposed by three rotating circular arc-walls in a straight channel. In the two-dimensional case, simple phenomenological arguments are used to estimate heuristically the mixing efficiency with two non-dimensional control parameters: the Strouhal number based on the bulk flow velocity, and the strength of the cross flow relative to the transport flow. The validity and limitations of the proposed mixing conditions are explained by the transport mechanisms in the mixer. The beneficial role of the elliptic flow regions for stretching and folding the passive scalar interfaces is highlighted, as well as a correlation between good mixing ability and the chaotic advection of tracers in the mixing zone.

A pressure-correction algorithm is presented for compressible fluid flow regimes. It is well-suited to simulate flows at all levels of Mach number with smooth and discontinuous flow field changes, by providing a precise representation of convective transport and acoustic propagation. The co-located finite volume space discretization is used with the AUSM flux splitting. It is demonstrated that two ingredients are essential for obtaining good quality solutions: the presence of an inertia term in the face velocity expression; a velocity difference diffusive term in the face pressure expression, with a correct Mach number scaling to recover the hydrodynamic and acoustic low Mach number limits. To meet these two requirements, a new flux scheme, named MIAU, for Momentum Interpolation with Advection Upstream splitting is proposed.

International audienceAn inertia term is introduced in the AUSM+-up scheme. The resulting scheme, called AUSM-IT (IT for Inertia Term), is designed as an extension of the AUSM+-up scheme allowing for full Mach number range calculations of unsteady flows including acoustic features. In line with the continuous asymptotic analysis, the AUSM-IT scheme satisfies the conservation of the discrete linear acoustic energy at first order in the low Mach number limit. Its capability to properly handle low Mach number unsteady flows, that may include acoustic waves or discontinuities, is numerically illustrated. The approach for building the AUSM-IT scheme from the AUSM+-up scheme is applicable to any other Godunov-type scheme