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Article Dans Une Revue Advances in Mathematical Sciences and Applications Année : 2019

A first-order bi-projection scheme for incompressible two-phase Bingham flows

Rénald Chalayer
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Thierry Dubois

Résumé

A first-order bi-projection scheme for the numerical simulation of two-phase im-miscible, incompressible and isothermal flows of viscoplastic media is presented. As in the Uzawa-like algorithm, the definition of the stress tensor is rewritten in terms of a pointwise projection. A pseudo-time relaxation term is added in order to obtain a geometric convergence of the fixed-point iterations used for the computation of the plastic part of the stress tensor. The coupling between pressure and velocity field is treated with a fractional time-stepping scheme. The interface between the two phases is handled with a level set formulation. Numerical simulations of Rayleigh-Taylor instabilities are performed and presented. The first order rate of convergence with respect to the time step is recovered both in the case of Newtonian and Bing-ham flows. Comparisons with published results in the case of Newtonian flows validate the parallel implementation of the bi-projection scheme.
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Dates et versions

hal-02138212 , version 1 (23-05-2019)

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  • HAL Id : hal-02138212 , version 1

Citer

Rénald Chalayer, Thierry Dubois. A first-order bi-projection scheme for incompressible two-phase Bingham flows. Advances in Mathematical Sciences and Applications, 2019, 28 (1), pp.155-169. ⟨hal-02138212⟩
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