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Modeling 3D Magma Dynamics Using a Discontinuous Galerkin Method

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  03 July 2015

Seshu Tirupathi ,
Jan S. Hesthaven  and
Yan Liang
Seshu Tirupathi*
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA IBM Research, Dublin, Damastown Industrial Park, Dublin 15, Ireland
Jan S. Hesthaven
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA EPFL-SB-MATHICSE-MCSS, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
Yan Liang
Affiliation:
Department of Geological Sciences, Brown University, Providence, RI 02912, USA
*
*Corresponding author. Email addresses: seshutir@ie.ibm.com (S. Tirupathi), jan.hesthaven@epfl.ch (J. S. Hesthaven), Yan_Liang@brown.edu (Y. Liang)
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Abstract

Discontinuous Galerkin (DG) and matrix-free finite element methods with a novel projective pressure estimation are combined to enable the numerical modeling of magma dynamics in 2D and 3D using the library deal.II. The physical model is an advection-reaction type system consisting of two hyperbolic equations to evolve porosity and soluble mineral abundance at local chemical equilibrium and one elliptic equation to recover global pressure. A combination of a discontinuous Galerkin method for the advection equations and a finite element method for the elliptic equation provide a robust and efficient solution to the channel regime problems of the physical system in 3D. A projective and adaptively applied pressure estimation is employed to significantly reduce the computational wall time without impacting the overall physical reliability in the modeling of important features of melt segregation, such as melt channel bifurcation in 2D and 3D time dependent simulations.

Keywords

magma dynamicsdiscontinuous Galerkin methodfinite element methodmatrix-free method

MSC classification

Secondary: 65Z05: Applications to physics 65M22: Solution of discretized equations 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 1 , July 2015 , pp. 230 - 246
Copyright
Copyright © Global-Science Press 2015 

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