Numerical modeling of magma-repository interactions

Onno Bokhove

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    Abstract

    This report explains the numerical programs behind a comprehensive modeling effort of magma-repository interactions. Magma-repository interactions occur when a magma dike with high-volatile content magma ascends through surrounding rock and encounters a tunnel or drift filled with either a magmatic gas or air at atmospheric pressure. The simplified mathematical model to describe these flow phenomena consists of compressible flow equations of one- or two-dimensional flow in a flow tube with a macroscopic equation of state relating the pressure to the density for a bubbly mixture of water in the liquid or vapor phase and the molten rock under isothermal conditions. These model equations are hyperbolic and consist of a conservative part and additional frictional and geometric terms. The latter geometric terms contain the influence of the varying cross section or width of the flow tube, and gravity. Two shock-capturing numerical methods, a Local Lax Friedrichs and an Essentially Non-Oscillatory scheme, are used to simulate these flows numerically. An extensive account is given of these two numerical methods and their validation for the magma flow application, including a comparison between various exact solutions and numerical solutions for idealized conditions. Finally, we give one- and two-dimensional reference simulations in more realistic flow geometries.
    Original languageEnglish
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Publication statusPublished - 2001

    Publication series

    NameMemorandum
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1610
    ISSN (Print)0169-2690

    Keywords

    • MSC-93A30
    • MSC-35L15
    • MSC-35L65
    • IR-65797
    • MSC-74A50
    • EWI-3430
    • MSC-74S20

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