Fast multigrid solution of the advection problem with closed characteristics

Irad Yavneh, Cornelis H. Venner, Achi Brandt

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    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
    Issue number1
    Publication statusPublished - 1998


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