A sharp Cartesian method for incompressible flows with large density ratios

Michel Bergmann 1 Lisl Weynans 1
1 MEMPHIS - Modeling Enablers for Multi-PHysics and InteractionS
Inria Bordeaux - Sud-Ouest, IMB - Institut de Mathématiques de Bordeaux
Abstract : A new Cartesian method for bifluid incompressible flows with high density ratios is presented. The specificity of the method relies on a sharp second order numerical scheme for the spatial resolution of the discontinuous elliptic problem for the pressure. The Navier-Stokes equations are integrated in time thanks to a fractional step method based on the Chorin scheme and discretized in space on a Cartesian mesh. The bifluid interface is implicitly represented using a level set function. The numerical tests show the improvements due to this sharp method compared to classical first order methods.
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Michel Bergmann, Lisl Weynans. A sharp Cartesian method for incompressible flows with large density ratios. [Research Report] RR-8926, INRIA Bordeaux. 2017, pp.23. ⟨hal-01331234v2⟩

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