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

Overview & Synopsis

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.