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Modeling Magma Dynamics with a Mixed Fourier Collocation — Discontinuous Galerkin Method

Published online by Cambridge University Press:  20 August 2015

Alan R. Schiemenz ,
Marc A. Hesse  and
Jan S. Hesthaven
Alan R. Schiemenz*
Affiliation:
Department of Geological Sciences, Brown University, Providence, RI 02910, USA Division of Applied Mathematics, Brown University, Providence, RI 02910, USA
Marc A. Hesse*
Affiliation:
Department of Geological Sciences, University of Texas at Austin, Austin, TX 78712, USA
Jan S. Hesthaven*
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI 02910, USA
*
Corresponding author.Email:alan.schiemenz@geophysik.uni-muenchen.de
Email:mhesse@jsg.utexas.edu
Email:Jan.Hesthaven@brown.edu
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Abstract

A high-order discretization consisting of a tensor product of the Fourier collocation and discontinuous Galerkin methods is presented for numerical modeling of magma dynamics. The physical model is an advection-reaction type system consisting of two hyperbolic equations and one elliptic equation. The high-order solution basis allows for accurate and efficient representation of compaction-dissolution waves that are predicted from linear theory. The discontinuous Galerkin method provides a robust and efficient solution to the eigenvalue problem formed by linear stability analysis of the physical system. New insights into the processes of melt generation and segregation, such as melt channel bifurcation, are revealed from two-dimensional time-dependent simulations.

Keywords

65Z0565M2265M7065T4065T50Magma dynamicsdiscontinuous Galerkin methodFourier collocation methodnumerical simulationslinear stability analysis
Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 2 , August 2011 , pp. 433 - 452
Copyright
Copyright © Global Science Press Limited 2011

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