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

J.A Mackenzie, W.R Mekwi

Research output: Contribution to journalArticle

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.
Original languageEnglish
Pages (from-to)888-905
Number of pages18
JournalIMA Journal of Numerical Analysis
Volume32
Issue number3
DOIs
Publication statusPublished - Jul 2012
Externally publishedYes

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Semidiscretization
Convection-diffusion
Unconditionally Stable
Convection-diffusion Equation
Adaptive Method
Time Integration
Conservation Laws
Governing equation
Conservation
Numerical Experiment
Scalar
Mesh
Finite Element
Formulation
Arbitrary
Experiments

Keywords

  • adaptivity
  • geometric conservation law
  • stability
  • ALE–FEM schemes
  • moving meshes
  • conversation law

Cite this

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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.",
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An unconditionally stable second-order accurate ALE–FEM scheme for two-dimensional convection–diffusion problems. / Mackenzie, J.A; Mekwi, W.R.

In: IMA Journal of Numerical Analysis, Vol. 32, No. 3, 07.2012, p. 888-905.

Research output: Contribution to journalArticle

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