An adaptive local grid refinement and peak/valley capture algorithm to solve nonlinear transport problems with moving sharp-fronts

    Authors

    F. Zhang; L. Jiang; G. T. Yeh;J. C. Parker

    Comments

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    Abbreviated Journal Title

    Transp. Porous Media

    Keywords

    nonlinear advection-dispersion-reaction equations; Lagrangian-Eulerian; decoupling method with an adaptive ZOOMing and Peak/valley Capture; (LEZOOMPC); Burger equation; multiphase flow; peak/valley capturing; adaptive local grid refinement; LAGRANGIAN-EULERIAN METHOD; EFFICIENT IMPLEMENTATION; EQUATIONS; SCHEMES; Engineering, Chemical

    Abstract

    Highly nonlinear advection-dispersion-reaction equations govern numerous transport phenomena. Robust, accurate, and efficient algorithms to solve these equations hold the key to the success of applying numerical models to field problems. This paper presents the development and verification of a computational algorithm to approximate the highly nonlinear transport equations of reactive chemical transport and multiphase flow. The algorithm was developed based on the Lagrangian-Eulerian decoupling method with an adaptive ZOOMing and Peak/valley Capture (LEZOOMPC) scheme. It consists of both backward and forward node tracking, rough element determination, peak/valley capturing, and adaptive local grid refinement. A second-order tracking was implemented to accurately and efficiently track all fictitious particles. Shanks' method was introduced to deal with slowly converging case. The accuracy and efficiency of the algorithm were verified with the Burger equation for a variety of cases. The robustness of the algorithm to achieve convergent solutions was demonstrated by highly nonlinear reactive contaminant transport and multiphase flow problems.

    Journal Title

    Transport in Porous Media

    Volume

    72

    Issue/Number

    1

    Publication Date

    1-1-2008

    Document Type

    Article

    Language

    English

    First Page

    53

    Last Page

    69

    WOS Identifier

    WOS:000252890100004

    ISSN

    0169-3913

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