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We consider the flow of a viscous incompressible fluid through a rigid
homogeneous porous medium. The permeability of the medium depends
on the pressure, so that the model is nonlinear. We propose a finite
element discretization of this problem and, in the case where the
dependence on the pressure is bounded from above and below, we prove
its convergence to the solution and propose an algorithm to solve
the discrete system. In the case where the dependence
on the pressure is exponential, we propose...
For a two phase incompressible flow we consider a diffuse interface model aimed at addressing the movement of three-phase (fluid-fluid-solid) contact lines. The model consists of the Cahn Hilliard Navier Stokes system with a variant of the Navier slip boundary conditions. We show that this model possesses a natural energy law. For this system, a new numerical technique based on operator splitting and fractional time-stepping is proposed. The method is shown to be unconditionally stable. We present...
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