A multiscale/stabilized formulation of the incompressible Navier-Stokes equations for moving boundary flows and fluid-structure interaction

Rooh A. Khurram, Arif Masud*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

92 Scopus citations

Abstract

This paper presents a multiscale/stabilized finite element formulation for the incompressible Navier-Stokes equations written in an Arbitrary Lagrangian-Eulerian (ALE) frame to model flow problems that involve moving and deforming meshes. The new formulation is derived based on the variational multiscale method proposed by Hughes (Comput Methods Appl Mech Eng 127:387-401, 1995) and employed in Masud and Khurram in (Comput Methods Appl Mech Eng 193:1997-2018, 2006); Masud and Khurram in (Comput Methods Appl Mech Eng 195:1750-1777, 2006) to study advection dominated transport phenomena. A significant feature of the formulation is that the structure of the stabilization terms and the definition of the stabilization tensor appear naturally via the solution of the sub-grid scale problem. A mesh moving technique is integrated in this formulation to accommodate the motion and deformation of the computational grid, and to map the moving boundaries in a rational way. Some benchmark problems are shown, and simulations of an elastic beam undergoing large amplitude periodic oscillations in a viscous fluid domain are presented.

Original languageEnglish (US)
Pages (from-to)403-416
Number of pages14
JournalComputational Mechanics
Volume38
Issue number4-5
DOIs
StatePublished - Sep 2006
Externally publishedYes

Keywords

  • Arbitrary Lagrangian-Eulerian (ALE) framework
  • Fluid-structure interaction (FSI)
  • Moving meshes
  • Multiscale finite element methods

ASJC Scopus subject areas

  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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