Sensitivity analysis of the grad-div stabilization parameter in finite element simulations of incompressible flow

Monika Neda, Faranak Pahlevani, Leo G. Rebholz, Jiajia Waters

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We present a numerical study of the sensitivity of the grad-div stabilization parameter for mixed finite element discretizations of incompressible flow problems. For incompressible isothermal and nonisothermal Stokes equations and Navier-Stokes equations, we develop the associated sensitivity equations for changes in the grad-div parameter. Finite element schemes are devised for computing solutions to the sensitivity systems, analyzed for stability and accuracy, and finally tested on several benchmark problems. Our results reveal that solutions are most sensitive for small values of the parameter, near obstacles and corners, when the pressure is large, and when the viscosity is small.

Original languageEnglish (US)
Pages (from-to)189-206
Number of pages18
JournalJournal of Numerical Mathematics
Volume24
Issue number3
DOIs
StatePublished - Oct 1 2016

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Incompressible flow
Finite Element Simulation
Incompressible Flow
Sensitivity analysis
Sensitivity Analysis
Stabilization
Navier Stokes equations
Stokes Equations
Mixed Finite Elements
Finite Element Discretization
Viscosity
Numerical Study
Navier-Stokes Equations
Benchmark
Finite Element
Computing

All Science Journal Classification (ASJC) codes

  • Computational Mathematics

Cite this

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abstract = "We present a numerical study of the sensitivity of the grad-div stabilization parameter for mixed finite element discretizations of incompressible flow problems. For incompressible isothermal and nonisothermal Stokes equations and Navier-Stokes equations, we develop the associated sensitivity equations for changes in the grad-div parameter. Finite element schemes are devised for computing solutions to the sensitivity systems, analyzed for stability and accuracy, and finally tested on several benchmark problems. Our results reveal that solutions are most sensitive for small values of the parameter, near obstacles and corners, when the pressure is large, and when the viscosity is small.",
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Sensitivity analysis of the grad-div stabilization parameter in finite element simulations of incompressible flow. / Neda, Monika; Pahlevani, Faranak; Rebholz, Leo G.; Waters, Jiajia.

In: Journal of Numerical Mathematics, Vol. 24, No. 3, 01.10.2016, p. 189-206.

Research output: Contribution to journalArticle

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