A stable and linear time discretization for a thermodynamically consistent model for two-phase incompressible flow.(English)Zbl 1329.76168
Summary: A new time discretization scheme for the numerical simulation of two-phase flow governed by a thermodynamically consistent diffuse interface model is presented. The scheme is consistent in the sense that it allows for a discrete in time energy inequality. An adaptive spatial discretization is proposed that conserves the energy inequality in the fully discrete setting by applying a suitable post processing step to the adaptive cycle. For the fully discrete scheme a quasi-reliable error estimator is derived which estimates the error both of the flow velocity, and of the phase field. The validity of the energy inequality in the fully discrete setting is numerically investigated.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76Txx | Multiphase and multicomponent flows |
| 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 |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
Keywords:
two-phase flow;diffuse-interface models;stable discretization scheme;Cahn-Hilliard Navier-Stokes model;adaptive meshingCite
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