A discontinuous Galerkin approximation for a wall-bounded consistent three-component Cahn-Hilliard flow model. (English) Zbl 1521.76353
Summary: We present a high-order discontinuous Galerkin (DG) discretization for the three-phase Cahn-Hilliard model of
[F. Boyer and C. Lapuerta, ESAIM, Math. Model. Numer. Anal. 40, No. 4, 653–687 (2006; Zbl 1173.35527)].
Study of a three component Cahn-Hilliard flow model]. In this model, consistency is ensured with an additional term in the chemical free-energy. The model considered in this work includes a wall boundary condition that allows for an arbitrary equilibrium contact angle in three-phase flows. The model is discretized with a high-order discontinuous Galerkin spectral element method that uses the symmetric interior penalty to compute the interface fluxes, and allows for unstructured meshes with curvilinear hexahedral elements. The integration in time uses a first order IMplicit-EXplicit (IMEX) method, such that the associated linear systems are decoupled for the two Cahn-Hilliard equations. Additionally, the Jacobian matrix is constant, and identical for both equations. This allows us to solve the two systems by performing only one LU factorization, with the size of the two-phase system, followed by two Gauss substitutions. Finally, we test numerically the accuracy of the scheme providing convergence analyses for two and three-dimensional cases, including the captive bubble test, the study of two bubbles in contact with a wall and the spinodal decomposition in a cube and in a curved pipe with a “T” junction.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 76D27 | Other free boundary flows; Hele-Shaw flows |
Citations:
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