Investigation of interpolation schemes for a class of nonlinear finite volume methods

Wenjuan Zhang, Mohammed Al Kobaisi, Huafeng Sun

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    Abstract

    The robustness and accuracy of a class of nonlinear finite volume methods (NFVM) for discretizing the heterogeneous and anisotropic pressure equation is investigated in this work. The formulation of NFVM requires the construction of one-sided fluxes, which involves interpolating pressure at auxiliary points. Grid vertices and harmonic averaging are two popular candidates. The principle of Enriched Multi-point Flux Approximation (EMPFA) is employed as an interpolating algorithm to interpolate pressure at grid vertices. To improve the robustness of interpolation using harmonic averaging point, a correction algorithm is proposed to modify those ill-placed harmonic averaging points so that all the co-normal vectors can be decomposed with non-negative coefficients successfully. Numerical tests demonstrate that the resulting NFVM has significantly improved robustness compared to NFVM utilizing the original harmonic averaging point and therefore can be applied to more general problems.

    Original languageBritish English
    Title of host publicationSimulation Series
    EditorsJose J. Padilla, Christopher J. Lynch
    Pages303-314
    Number of pages12
    Edition10
    ISBN (Electronic)9781510860230
    StatePublished - 2018
    Event50th Summer Computer Simulation Conference, SCSC 2018, Part of the 2018 Summer Simulation Multi-Conference, SummerSim 2018 - Bordeaux, France
    Duration: 9 Jul 201812 Jul 2018

    Publication series

    NameSimulation Series
    Number10
    Volume50
    ISSN (Print)0735-9276

    Conference

    Conference50th Summer Computer Simulation Conference, SCSC 2018, Part of the 2018 Summer Simulation Multi-Conference, SummerSim 2018
    Country/TerritoryFrance
    CityBordeaux
    Period9/07/1812/07/18

    Keywords

    • Anisotropic diffusion equation
    • Harmonic averaging point
    • Nonlinear finite volume method

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