Convergence of numerical approximations of the incompressible Navier-Stokes equations with variable density and viscosity

Chun Liu, Noel J. Walkington

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

We consider numerical approximations of incompressible Newtonian fluids having variable, possibly discontinuous, density and viscosity. Since solutions of the equations with variable density and viscosity may not be unique, numerical schemes may not converge. If the solution is unique, then approximate solutions computed using the discontinuous Galerkin method to approximate the convection of the density and stable finite element approximations of the momentum equation converge to the solution. If the solution is not unique, a subsequence of these approximate solutions will converge to a solution.

Original languageEnglish (US)
Pages (from-to)1287-1304
Number of pages18
JournalSIAM Journal on Numerical Analysis
Volume45
Issue number3
DOIs
StatePublished - Dec 1 2007

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Incompressible Navier-Stokes Equations
Numerical Approximation
Navier Stokes equations
Viscosity
Converge
Approximate Solution
Discontinuous Galerkin Method
Newtonian Fluid
Finite Element Approximation
Subsequence
Incompressible Fluid
Numerical Scheme
Convection
Galerkin methods
Momentum
Fluids

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

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Convergence of numerical approximations of the incompressible Navier-Stokes equations with variable density and viscosity. / Liu, Chun; Walkington, Noel J.

In: SIAM Journal on Numerical Analysis, Vol. 45, No. 3, 01.12.2007, p. 1287-1304.

Research output: Contribution to journalArticle

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