One time-step finite element discretization of the equation of motion of two-fluid flows. (English) Zbl 1089.76032

Summary: We discretize in space the equations obtained at each time step when discretizing in time a Navier-Stokes system modelling the two-dimensional flow in a horizontal pipe of two immiscible fluids with comparable densities, but very different viscosities. At each time step the system reduces to a generalized Stokes problem with nonstandard conditions at the boundary and at the interface between the two fluids. We discretize this system with the mini-element and establish error estimates.


76M10 Finite element methods applied to problems in fluid mechanics
76T10 Liquid-gas two-phase flows, bubbly flows
76D05 Navier-Stokes equations for incompressible viscous fluids
76D45 Capillarity (surface tension) for incompressible viscous fluids
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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