A fourth-order-accurate difference approximation for the incompressible Navier-Stokes equations

We discuss fourth-order-accurate difference approximations for parabolic systems and for the incompressible Navier—Stokes equations. A general principle for deriving numerical boundary conditions for higher-order-accurate difference schemes is described. Some difference approximations for parabolic...

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Published inComputers & fluids Vol. 23; no. 4; pp. 575 - 593
Main Authors Henshaw, William D., Kreiss, Heinz-Otto, Reyna, Luis G.M.
Format Journal Article
LanguageEnglish
Published Oxford Elsevier Ltd 1994
Elsevier Science
Subjects
Computational methods in fluid dynamics
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Physics
Boundary conditions
Three-dimensional calculations
Incompressible fluid
Numerical solution
Navier-Stokes equations
Finite difference method
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Abstract We discuss fourth-order-accurate difference approximations for parabolic systems and for the incompressible Navier—Stokes equations. A general principle for deriving numerical boundary conditions for higher-order-accurate difference schemes is described. Some difference approximations for parabolic systems are analyzed for stability and accuracy. The principle is used to derive stable and accurate numerical boundary conditions for the incompressible Navier—Stokes equations. Numerical results are given from a fourth-order-accurate scheme for the incompressible Navier—Stokes equations on overlapping grids in two- and three-space dimensions.
AbstractList We discuss fourth-order-accurate difference approximations for parabolic systems and for the incompressible Navier—Stokes equations. A general principle for deriving numerical boundary conditions for higher-order-accurate difference schemes is described. Some difference approximations for parabolic systems are analyzed for stability and accuracy. The principle is used to derive stable and accurate numerical boundary conditions for the incompressible Navier—Stokes equations. Numerical results are given from a fourth-order-accurate scheme for the incompressible Navier—Stokes equations on overlapping grids in two- and three-space dimensions.
Author Kreiss, Heinz-Otto
Reyna, Luis G.M.
Henshaw, William D.
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  givenname: Luis G.M.
  surname: Reyna
  fullname: Reyna, Luis G.M.
  organization: IBM Research Division, T.J. Watson Research Centre, P.O. Box 218, Yorktown Heights, NY 10598, U.S.A
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Cites_doi 10.1016/0021-9991(90)90196-8
10.1002/fld.1650071008
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Issue 4
Keywords Boundary conditions
Three-dimensional calculations
Incompressible fluid
Numerical solution
Navier-Stokes equations
Finite difference method
Language English
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References Gresho, Sani (BIB4) 1987; 7
Henshaw (BIB5) 1992
Strikwerda (BIB3) 1989
Ladyzhenskaya (BIB6) 1963
Kreiss, Lorenz (BIB2) 1989
Chesshire, Henshaw (BIB1) 1990; 90
Strikwerda (10.1016/0045-7930(94)90053-1_BIB3) 1989
Gresho (10.1016/0045-7930(94)90053-1_BIB4) 1987; 7
Chesshire (10.1016/0045-7930(94)90053-1_BIB1) 1990; 90
Henshaw (10.1016/0045-7930(94)90053-1_BIB5) 1992
Kreiss (10.1016/0045-7930(94)90053-1_BIB2) 1989
Ladyzhenskaya (10.1016/0045-7930(94)90053-1_BIB6) 1963
References_xml – year: 1989
  ident: BIB2
  publication-title: Initial-boundary Value Problems and the Navier Stokes Equations
  contributor:
    fullname: Lorenz
– year: 1989
  ident: BIB3
  publication-title: Finite Difference Schemes and Partial Differential Equations
  contributor:
    fullname: Strikwerda
– year: 1963
  ident: BIB6
  publication-title: The Mathematical Theory of Viscous Incompressible Flow
  contributor:
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– year: 1992
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  article-title: A fourth-order accurate method for the incompressible Navier-Stokes equations on overlapping grids
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  contributor:
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– volume: 7
  start-page: 1111
  year: 1987
  ident: BIB4
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  article-title: Composite overlapping meshes for the solution of partial differential equations
  publication-title: J. Comput. Phys.
  contributor:
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– year: 1989
  ident: 10.1016/0045-7930(94)90053-1_BIB3
  contributor:
    fullname: Strikwerda
– volume: 90
  start-page: 1
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  ident: 10.1016/0045-7930(94)90053-1_BIB1
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  ident: 10.1016/0045-7930(94)90053-1_BIB6
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– volume: 7
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  ident: 10.1016/0045-7930(94)90053-1_BIB4
  article-title: On the pressure boundary conditions for the incompressible Navier-Stokes equations
  publication-title: Int. J. Numer. Meth. Fluids
  doi: 10.1002/fld.1650071008
  contributor:
    fullname: Gresho
– year: 1992
  ident: 10.1016/0045-7930(94)90053-1_BIB5
  article-title: A fourth-order accurate method for the incompressible Navier-Stokes equations on overlapping grids
  contributor:
    fullname: Henshaw
– year: 1989
  ident: 10.1016/0045-7930(94)90053-1_BIB2
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    fullname: Kreiss
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Snippet We discuss fourth-order-accurate difference approximations for parabolic systems and for the incompressible Navier—Stokes equations. A general principle for...
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SubjectTerms Computational methods in fluid dynamics
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Physics
Title A fourth-order-accurate difference approximation for the incompressible Navier-Stokes equations
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