An XFEM-based embedding mesh technique for incompressible viscous flows

Shadan Shahmiri, Axel Gerstenberger, Wolfgang A. Wall

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

This paper presents a finite element (FE) embedding mesh technique to efficiently embed arbitrary fluid mesh patches into Cartesian or unstructured background fluid grids. Our motivating application for such a technique is to efficiently resolve flow features like boundary layers around structures, which is achieved by attaching fluid boundary layer meshes around these structure surfaces. The proposed technique can be classified as a non-overlapping domain decomposition method. The particular feature is that the embedded patch cuts a void region into the background grid independently of background element edges. Since the embedded fluid domain ends in the middle of background elements, extended FE techniques are used to model a sharp separation between active and inactive regions on the background grid. The active background region is coupled to the boundary layer mesh using a mixed/hybrid Lagrange multiplier technique as proposed in Gerstenberger and Wall (textitInt. J. Numer. Meth. Engng. 2010; 82:537-563). The coupling formulation works without stabilization for the Lagrange multiplier unknowns and the Lagrange multiplier can be completely condensed on the element level. Within this paper, the approach is derived for incompressible, viscous flows. Three-dimensional examples using linear and quadratic shape functions demonstrate the correctness and the versatility of the proposed approach.

Original languageEnglish
Pages (from-to)166-190
Number of pages25
JournalInternational Journal for Numerical Methods in Fluids
Volume65
Issue number1-3
DOIs
StatePublished - Jan 2011

Keywords

  • Cartesian grid
  • Domain decomposition
  • Embedded Dirichlet condition
  • Embedded meshes
  • Extended finite element method
  • Fixed grid
  • Fluid-structure interaction
  • Incompressible Navier-Stokes equations
  • Surface coupling

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