A stabilized and coupled meshfree/meshbased method for the incompressible Navier-Stokes equations-Part I: Stabilization

Thomas Peter Fries, Hermann Georg Matthies

Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

Abstract

A stabilized meshfree Galerkin method is employed for the approximation of the incompressible Navier-Stokes equations in Eulerian or arbitrary Lagrangian-Eulerian (ALE) formulation. Equal-order interpolations for velocities and pressure are used. It is well-known from the meshbased context, i.e. from finite volume and finite element methods, that in convection-dominated flow problems in Eulerian or ALE formulation, stabilization is a crucial requirement for reliable solutions. Also, stabilization is needed in order to enable equal-order interpolations of the incompressible Navier-Stokes equations. Standard stabilization techniques, developed in a meshbased context, are extended to meshfree methods. It is found that the same structure of the stabilization schemes may be used, however the aspect of the stabilization parameter, weighting the stabilization terms, has to be reconsidered. In Part II of this work, the resulting stabilized meshfree Galerkin method is coupled with a stabilized finite element method. The resulting coupled method employs the comparatively costly meshfree Galerkin method only where it is needed-i.e. in areas of the domain, where a mesh is difficult to maintain-and the efficient meshbased finite element method is used in the rest of the domain. The fluid solver resulting from this technique is able to solve complex flow problems, involving large deformations of the physical domain and/or moving and rotating obstacles.

Originalspracheenglisch
Seiten (von - bis)6205-6224
Seitenumfang20
FachzeitschriftComputer Methods in Applied Mechanics and Engineering
Jahrgang195
Ausgabenummer44-47
DOIs
PublikationsstatusVeröffentlicht - 15 Sep 2006

Fingerprint

meshfree methods
Navier-Stokes equation
Navier Stokes equations
Stabilization
stabilization
Galerkin method
Galerkin methods
finite element method
Finite element method
interpolation
Interpolation
formulations
mesh
convection
requirements
Fluids
fluids
approximation

Schlagwörter

    ASJC Scopus subject areas

    • !!Computer Science Applications
    • !!Computational Mechanics

    Dies zitieren

    A stabilized and coupled meshfree/meshbased method for the incompressible Navier-Stokes equations-Part I : Stabilization. / Fries, Thomas Peter; Matthies, Hermann Georg.

    in: Computer Methods in Applied Mechanics and Engineering, Jahrgang 195, Nr. 44-47, 15.09.2006, S. 6205-6224.

    Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

    @article{e5db49eecddb49328646fbb368349352,
    title = "A stabilized and coupled meshfree/meshbased method for the incompressible Navier-Stokes equations-Part I: Stabilization",
    abstract = "A stabilized meshfree Galerkin method is employed for the approximation of the incompressible Navier-Stokes equations in Eulerian or arbitrary Lagrangian-Eulerian (ALE) formulation. Equal-order interpolations for velocities and pressure are used. It is well-known from the meshbased context, i.e. from finite volume and finite element methods, that in convection-dominated flow problems in Eulerian or ALE formulation, stabilization is a crucial requirement for reliable solutions. Also, stabilization is needed in order to enable equal-order interpolations of the incompressible Navier-Stokes equations. Standard stabilization techniques, developed in a meshbased context, are extended to meshfree methods. It is found that the same structure of the stabilization schemes may be used, however the aspect of the stabilization parameter, weighting the stabilization terms, has to be reconsidered. In Part II of this work, the resulting stabilized meshfree Galerkin method is coupled with a stabilized finite element method. The resulting coupled method employs the comparatively costly meshfree Galerkin method only where it is needed-i.e. in areas of the domain, where a mesh is difficult to maintain-and the efficient meshbased finite element method is used in the rest of the domain. The fluid solver resulting from this technique is able to solve complex flow problems, involving large deformations of the physical domain and/or moving and rotating obstacles.",
    keywords = "Coupled, Fluid, Meshfree, Stabilization",
    author = "Fries, {Thomas Peter} and Matthies, {Hermann Georg}",
    year = "2006",
    month = "9",
    day = "15",
    doi = "10.1016/j.cma.2005.12.002",
    language = "English",
    volume = "195",
    pages = "6205--6224",
    journal = "Computer Methods in Applied Mechanics and Engineering",
    issn = "0045-7825",
    publisher = "Elsevier B.V.",
    number = "44-47",

    }

    TY - JOUR

    T1 - A stabilized and coupled meshfree/meshbased method for the incompressible Navier-Stokes equations-Part I

    T2 - Stabilization

    AU - Fries, Thomas Peter

    AU - Matthies, Hermann Georg

    PY - 2006/9/15

    Y1 - 2006/9/15

    N2 - A stabilized meshfree Galerkin method is employed for the approximation of the incompressible Navier-Stokes equations in Eulerian or arbitrary Lagrangian-Eulerian (ALE) formulation. Equal-order interpolations for velocities and pressure are used. It is well-known from the meshbased context, i.e. from finite volume and finite element methods, that in convection-dominated flow problems in Eulerian or ALE formulation, stabilization is a crucial requirement for reliable solutions. Also, stabilization is needed in order to enable equal-order interpolations of the incompressible Navier-Stokes equations. Standard stabilization techniques, developed in a meshbased context, are extended to meshfree methods. It is found that the same structure of the stabilization schemes may be used, however the aspect of the stabilization parameter, weighting the stabilization terms, has to be reconsidered. In Part II of this work, the resulting stabilized meshfree Galerkin method is coupled with a stabilized finite element method. The resulting coupled method employs the comparatively costly meshfree Galerkin method only where it is needed-i.e. in areas of the domain, where a mesh is difficult to maintain-and the efficient meshbased finite element method is used in the rest of the domain. The fluid solver resulting from this technique is able to solve complex flow problems, involving large deformations of the physical domain and/or moving and rotating obstacles.

    AB - A stabilized meshfree Galerkin method is employed for the approximation of the incompressible Navier-Stokes equations in Eulerian or arbitrary Lagrangian-Eulerian (ALE) formulation. Equal-order interpolations for velocities and pressure are used. It is well-known from the meshbased context, i.e. from finite volume and finite element methods, that in convection-dominated flow problems in Eulerian or ALE formulation, stabilization is a crucial requirement for reliable solutions. Also, stabilization is needed in order to enable equal-order interpolations of the incompressible Navier-Stokes equations. Standard stabilization techniques, developed in a meshbased context, are extended to meshfree methods. It is found that the same structure of the stabilization schemes may be used, however the aspect of the stabilization parameter, weighting the stabilization terms, has to be reconsidered. In Part II of this work, the resulting stabilized meshfree Galerkin method is coupled with a stabilized finite element method. The resulting coupled method employs the comparatively costly meshfree Galerkin method only where it is needed-i.e. in areas of the domain, where a mesh is difficult to maintain-and the efficient meshbased finite element method is used in the rest of the domain. The fluid solver resulting from this technique is able to solve complex flow problems, involving large deformations of the physical domain and/or moving and rotating obstacles.

    KW - Coupled

    KW - Fluid

    KW - Meshfree

    KW - Stabilization

    UR - http://www.scopus.com/inward/record.url?scp=33746192400&partnerID=8YFLogxK

    U2 - 10.1016/j.cma.2005.12.002

    DO - 10.1016/j.cma.2005.12.002

    M3 - Article

    VL - 195

    SP - 6205

    EP - 6224

    JO - Computer Methods in Applied Mechanics and Engineering

    JF - Computer Methods in Applied Mechanics and Engineering

    SN - 0045-7825

    IS - 44-47

    ER -