Fast multigrid solution of the advection problem with closed characteristics

Irad Yavneh, Cornelis H. Venner, Achi Brandt

    Research output: Contribution to journalArticleAcademicpeer-review

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    Abstract

    The numerical solution of the advection-diffusion problem in the inviscid limit with closed characteristics is studied as a prelude to an efficient high Reynolds-number flow solver. It is demonstrated by a heuristic analysis and numerical calculations that using upstream discretization with downstream relaxation ordering in a multigrid cycle with appropriate residual weighting leads to an efficient solution process. Upstream finite-difference approximations to the advection operator are derived whose truncation terms approximate "physical" (Laplacian) viscosity, thus avoiding spurious solutions to the homogeneous problem when the artificial diffusivity dominates the physical viscosity [A. Brandt and I. Yavneh, J. Comput. Phys., 93 (1991), pp. 128--143].
    Original languageEnglish
    Pages (from-to)111-125
    JournalSIAM journal on scientific computing
    Volume19
    Issue number1
    DOIs
    Publication statusPublished - 1998

    Fingerprint

    Advection
    Viscosity
    Spurious Solutions
    Inviscid Limit
    Closed
    Advection-diffusion
    Finite Difference Approximation
    Diffusion Problem
    Diffusivity
    Efficient Solution
    Truncation
    Numerical Calculation
    Weighting
    Reynolds number
    Discretization
    Numerical Solution
    Heuristics
    Cycle
    Term
    Operator

    Cite this

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    abstract = "The numerical solution of the advection-diffusion problem in the inviscid limit with closed characteristics is studied as a prelude to an efficient high Reynolds-number flow solver. It is demonstrated by a heuristic analysis and numerical calculations that using upstream discretization with downstream relaxation ordering in a multigrid cycle with appropriate residual weighting leads to an efficient solution process. Upstream finite-difference approximations to the advection operator are derived whose truncation terms approximate {"}physical{"} (Laplacian) viscosity, thus avoiding spurious solutions to the homogeneous problem when the artificial diffusivity dominates the physical viscosity [A. Brandt and I. Yavneh, J. Comput. Phys., 93 (1991), pp. 128--143].",
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    Fast multigrid solution of the advection problem with closed characteristics. / Yavneh, Irad; Venner, Cornelis H.; Brandt, Achi.

    In: SIAM journal on scientific computing, Vol. 19, No. 1, 1998, p. 111-125.

    Research output: Contribution to journalArticleAcademicpeer-review

    TY - JOUR

    T1 - Fast multigrid solution of the advection problem with closed characteristics

    AU - Yavneh, Irad

    AU - Venner, Cornelis H.

    AU - Brandt, Achi

    PY - 1998

    Y1 - 1998

    N2 - The numerical solution of the advection-diffusion problem in the inviscid limit with closed characteristics is studied as a prelude to an efficient high Reynolds-number flow solver. It is demonstrated by a heuristic analysis and numerical calculations that using upstream discretization with downstream relaxation ordering in a multigrid cycle with appropriate residual weighting leads to an efficient solution process. Upstream finite-difference approximations to the advection operator are derived whose truncation terms approximate "physical" (Laplacian) viscosity, thus avoiding spurious solutions to the homogeneous problem when the artificial diffusivity dominates the physical viscosity [A. Brandt and I. Yavneh, J. Comput. Phys., 93 (1991), pp. 128--143].

    AB - The numerical solution of the advection-diffusion problem in the inviscid limit with closed characteristics is studied as a prelude to an efficient high Reynolds-number flow solver. It is demonstrated by a heuristic analysis and numerical calculations that using upstream discretization with downstream relaxation ordering in a multigrid cycle with appropriate residual weighting leads to an efficient solution process. Upstream finite-difference approximations to the advection operator are derived whose truncation terms approximate "physical" (Laplacian) viscosity, thus avoiding spurious solutions to the homogeneous problem when the artificial diffusivity dominates the physical viscosity [A. Brandt and I. Yavneh, J. Comput. Phys., 93 (1991), pp. 128--143].

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