An unconditionally stable second-order accurate ALE–FEM scheme for two-dimensional convection–diffusion problems

John Mackenzie, W.R. Mekwi

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

The aim of this paper is to investigate the stability of time integration schemes for the solution of a finite element semi-discretization of a scalar convection–diffusion equation defined on a moving domain. An arbitrary Lagrangian–Eulerian formulation is used to reformulate the governing equation with respect to a moving reference frame. We devise an adaptive θ-method time integrator that is shown to be unconditionally stable and asymptotically second-order accurate for smoothly evolving meshes. An essential feature of the method is that it satisfies a discrete equivalent of the well-known geometric conservation law. Numerical experiments are presented to confirm the findings of the analysis.
LanguageEnglish
Pages888-905
Number of pages18
JournalIMA Journal of Numerical Analysis
Volume32
Issue number3
Early online date19 Sep 2011
DOIs
Publication statusPublished - 2012

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θ-method
Semidiscretization
Convection-diffusion Problems
Unconditionally Stable
Convection-diffusion Equation
Time Integration
Conservation Laws
Governing equation
Conservation
Numerical Experiment
Scalar
Mesh
Finite Element
Finite element method
Formulation
Arbitrary
Experiments
Convection

Keywords

  • adaptivity
  • moving meshes
  • ALE-FEMschemes
  • stability geometric conservation law

Cite this

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AB - The aim of this paper is to investigate the stability of time integration schemes for the solution of a finite element semi-discretization of a scalar convection–diffusion equation defined on a moving domain. An arbitrary Lagrangian–Eulerian formulation is used to reformulate the governing equation with respect to a moving reference frame. We devise an adaptive θ-method time integrator that is shown to be unconditionally stable and asymptotically second-order accurate for smoothly evolving meshes. An essential feature of the method is that it satisfies a discrete equivalent of the well-known geometric conservation law. Numerical experiments are presented to confirm the findings of the analysis.

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KW - moving meshes

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KW - stability geometric conservation law

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