A discontinuous Galerkin approximation for a wall–bounded consistent three–component Cahn–Hilliard flow model
| Autor: | Gonzalo Rubio, Ángel Rivero–Jiménez, Esteban Ferrer, Carlos Redondo, Juan Manzanero |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
General Computer Science
Discretization 01 natural sciences 010305 fluids & plasmas law.invention Physics::Fluid Dynamics symbols.namesake multiphysics law Discontinuous Galerkin method 0103 physical sciences Boundary value problem 0101 mathematics Mathematics Curvilinear coordinates discontinuous galerkin schemes multiflows Mathematical analysis Linear system General Engineering simulation LU decomposition 010101 applied mathematics high order schemes Jacobian matrix and determinant symbols Hexahedron |
| Zdroj: | Research article |
| DOI: | 10.5281/zenodo.3749877 |
| Popis: | We present an efficient high–order discontinuous Galerkin (DG) discretization for the three–phase Cahn–Hilliard system. Among the different approaches, we use the model derived in [Boyer, F., & Lapuerta, C. (2006). Study of a three component Cahn–Hilliard flow model], where the 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 to be solved. Additionally, the Jacobian matrix is constant, and identical for both equations. This allows an efficient resolution of the two systems by performing only one LU factorization of the size of the two–phase system and two Gauss substitutions. Finally, we test numerically the accuracy of the scheme with a convergence analysis, the captive bubble test and a study of two bubbles in contact with a wall |
| Databáze: | OpenAIRE |
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