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Volume 18, Issue 1
Modeling 3D Magma Dynamics Using a Discontinuous Galerkin Method

Seshu Tirupathi, Jan S. Hesthaven & Yan Liang

DOI: 10.4208/cicp.090314.151214a

Commun. Comput. Phys., 18 (2015), pp. 230-246.

Published online: 2018-04

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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.

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@Article{CiCP-18-230, author = {}, title = {Modeling 3D Magma Dynamics Using a Discontinuous Galerkin Method}, journal = {Communications in Computational Physics}, year = {2018}, volume = {18}, number = {1}, pages = {230--246}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.090314.151214a}, url = {http://global-sci.org/intro/article_detail/cicp/11026.html} }
TY - JOUR T1 - Modeling 3D Magma Dynamics Using a Discontinuous Galerkin Method JO - Communications in Computational Physics VL - 1 SP - 230 EP - 246 PY - 2018 DA - 2018/04 SN - 18 DO - http://doi.org/10.4208/cicp.090314.151214a UR - https://global-sci.org/intro/article_detail/cicp/11026.html KW - AB -

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.

Seshu Tirupathi, Jan S. Hesthaven & Yan Liang. (2020). Modeling 3D Magma Dynamics Using a Discontinuous Galerkin Method. Communications in Computational Physics. 18 (1). 230-246. doi:10.4208/cicp.090314.151214a
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