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Two-phase flow with mass density contrast: stable schemes for a thermodynamic consistent and frame-indifferent diffuse-interface model.(English)Zbl 1349.76210

Summary: In this paper, we present a numerical scheme for the diffuse-interface model in [H. Abels et al., Math. Models Methods Appl. Sci. 22, No. 3, 1150013, 40 p. (2012;Zbl 1242.76342)] for two-phase flow of immiscible, incompressible fluids. As that model is in particular consistent with thermodynamics, energy estimates are expected to carry over to the discrete setting. By a subtle discretization of the convective coupling with the flux of the phase-field in the momentum equation, we prove discrete consistency with thermodynamics. Numerical experiments in two spatial dimensions – ranging from Rayleigh-Taylor instability to a comparison with previous modeling approaches – indicate the full practicality of our scheme and enable a first validation of the new modeling approach in [loc. cit.].

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76M12 Finite volume methods applied to problems in fluid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
76T99 Multiphase and multicomponent flows

Citations:

Zbl 1242.76342

Software:

PARDISO

Cite

References:

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[3]Abels, H.; Garcke, H.; Grün, G., Thermodynamically consistent, frame indifferent diffuse interface models for incompressible two-phase flows with different densities, Math. Models Methods Appl. Sci., 22, 3, 1150013 (2012) ·Zbl 1242.76342
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[13]Grün, G.; Klingbeil, F., On stable schemes for diffuse interface models for two-phase flow with general mass densities (2011), University of Erlangen, preprint ·Zbl 1349.76210
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[25]Schenk, O.; Gärtner, K., Solving unsymmetric sparse systems of linear equations with PARDISO, Future Gener. Comput. Syst., 20, 475-487 (2004)
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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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