A comparison between the XFEM and a boundary-fitted mesh method for the simulation of rigid particles in Cahn-Hilliard fluids

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Abstract

Two distinct numerical methods are compared for the simulation of rigid particles sus- pended in Cahn-Hilliard fluids: a boundary-fitted mesh method (BFMM) and an extended finite element method (XFEM). In the BFMM, meshes are generated that cover only the fluid domain and are aligned with the particle boundary, thus boundary conditions can be imposed directly in the nodes on the particle boundary. In the XFEM, a mesh is generated that covers both the fluid and particle domain, and accurate integration is performed by subdividing elements that are intersected by the particle boundary. Furthermore, boundary conditions on the particle boundary are imposed in a weak sense.
In the BFMM, locally refined meshes are generated, and remeshing is performed when the fluid-fluid interface moves out of the refined region. In the XFEM, a grid deformation technique is used to locally refine the mesh. This approach avoids the generation of new meshes, but allows for less control over the local element size. Excellent agreement was found between the two methods. In terms of accuracy, both methods perform similar, with the BFMM being slightly more accurate when studying mesh-convergence and the XFEM being slightly more accurate when studying time-convergence.
Original languageEnglish
Pages (from-to)121-136
Number of pages16
JournalComputers & Fluids
Volume148
DOIs
Publication statusPublished - 22 Apr 2017

Keywords

  • Boundary-fitted meshes
  • Cahn–Hilliard
  • Diffuse-interface
  • Extended finite element method
  • Finite element method
  • Suspended particles

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