Modeling 3D Magma Dynamics Using a Discontinuous Galerkin Method

Tirupathi, Seshu; Hesthaven, Jan S.; Liang, Yan

doi:10.4208/cicp.090314.151214a

Cited by 6 publications

(12 citation statements)

References 18 publications

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“…II uses the PETSc package (Balay et al, 1997) for parallel computation. Our code has recently been used to model reactive dissolution in the upwelling mantle in both 2-D and 3-D (Tirupathi et al, 2014). deal.…”

Section: Numerical Scheme and Methodsmentioning

confidence: 99%

Melt Segregation and Depletion During Ascent of Buoyant Diapirs in Subduction Zones

et al. 2020

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Cold, low‐density diapirs arising from hydrated mantle and/or subducted sediments on the top of subducting slabs have been invoked to transport key chemical signatures to the source region of arc magmas. However, to date there have been few quantitative models to constrain melting in such diapirs. Here we use a two‐phase Darcy‐Stokes‐energy model to investigate thermal evolution, melting, and depletion in a buoyant sediment diapir ascending through the mantle wedge. Using a simplified 2‐D circular geometry, we investigate diapir evolution in three scenarios with increasing complexity. In the first two scenarios we consider instantaneous heating of a diapir by thermal diffusion with and without the effect of the latent heat of melting. Then, these simplified calculations are compared to numerical simulations that include melting, melt segregation, and the influence of depletion on the sediment solidus along pressure‐temperature‐time (P‐T‐t) paths appropriate for ascent through the mantle wedge. The high boundary temperature induces a rim of high porosity, into which new melts are focused and then migrate upward. The rim thus acts like an annulus melt channel, while the effect of depletion buffers additional melt production. Solid matrix flow combined with recrystallization of melt pooled near the top of the diapir can result in large gradients in depletion across the diapir. These large depletion gradients can either be preserved if the diapir leaks melt during ascent, or rehomogenized in a sealed diapir. Overall our numerical simulations predict less melt production than the simplified thermal diffusion calculations. Specifically, we show that diapirs whose ascent paths favor melting beneath the volcanic arc will undergo no more than ~40–50% total melting.

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Section: Numerical Scheme and Methodsmentioning

confidence: 99%

Melt Segregation and Depletion During Ascent of Buoyant Diapirs in Subduction Zones

et al. 2020

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“…This higher than background porosity at the inflow is attributed to higher abundance of fusible materials in the upwelling mantle column [27]. The methods described in this paper can be easily extended to 3D as well using deal.II which provides a modern interface for dimension independent programming and adaptive mesh refinement [43,44]. Geological applications of reactive melt migration in 2D and 3D using the numerical methods outlined in this study and those in [43,44] will be presented in a companion study.…”

Section: Discussionmentioning

confidence: 99%

Multilevel and local time-stepping discontinuous Galerkin methods for magma dynamics

et al. 2015

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Discontinuous Galerkin (DG) method is presented for numerical modeling of melt migration in a chemically reactive and viscously deforming upwelling mantle column at local chemical equilibrium. DG methods for both advection and elliptic equations provide a robust and efficient solution to the problems of melt migration in the asthenospheric upper mantle. Assembling and solving the elliptic equation is the major bottleneck in these computations. To address this issue, adaptive mesh refinement and local time-stepping methods have been proposed to improve the computational wall time. The robustness of DG methods is demonstrated through two benchmark problems by modeling detailed structure of high-porosity dissolution channels and compaction dissolution waves.

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“…The nondimensionalized equations are solved numerically using a high‐order accurate scheme that consists of a fourth‐order Discontinuous Galerkin (DG) method for spatial discretization and a third‐order low‐storage explicit Runge Kutta method for the time integration [ Schiemenz et al ., ; Tirupathi , ; Tirupathi et al ., ]. The numerical scheme is implemented using the finite element software deal.II [ Bangherth et al ., ].…”

Section: Model Setupmentioning

confidence: 99%

A high‐order numerical study of reactive dissolution in an upwelling heterogeneous mantle: 2. Effect of shear deformation

Baltzell

Parmentier

Liang

et al. 2015

Geochem Geophys Geosyst

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High-porosity dunite channels produced by orthopyroxene dissolution may provide pathways for orthopyroxene-undersaturated melt generated in the deep mantle to reach shallower depth without extensive chemical reequilibration with surrounding mantle. Previous studies have considered these highporosity channels and melt localization in the presence of a uniform upwelling mantle flow through the process of melt-rock reaction as well as shear deformation, but not both simultaneously. In this Part 2 of a numerical study of high-porosity melt and dunite channel formation during reactive dissolution, we considered the effect of shear deformation on channel distribution and channel geometry in an upwelling and viscously compacting mantle column. We formulated a high-order numerical experiment using conditions similar to those in Part 1, but with an additional prescribed horizontal shearing component in the solid matrix, as could be present in flowing mantle beneath spreading centers. Our focus was to examine orthopyroxene dissolution to determine the behavior of dunite formation and its interaction with melt flow field, by varying the upwelling and shear rate, orthopyroxene solubility gradient, and domain height. Introduction of shearing tilts the developing dunite, causing asymmetry in the orthopyroxene gradient between the dunite channels and the surrounding harzburgite. The downwind gradient is sharp, nearly discontinuous, whereas the upwind gradient is more gradual. For higher shear rates, a wave-like pattern of alternating high and low-porosity bands form on the downwind side of the channel. The band spacing increases with increasing shear rate, relative melt flow rate, and orthopyroxene solubility gradient, whereas the band angle is independent of solubility gradient and increases with increasing shear rate and decreasing relative melt flow rate. Such features could be observable in the field and provide evidence for mantle shearing. Standing wave-like patterns of melt fraction also develop on the downwind side with possible implications for the interpretation of seismic velocities in upwelling mantle.

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Modeling 3D Magma Dynamics Using a Discontinuous Galerkin Method

Cited by 6 publications

References 18 publications

Melt Segregation and Depletion During Ascent of Buoyant Diapirs in Subduction Zones

Melt Segregation and Depletion During Ascent of Buoyant Diapirs in Subduction Zones

Multilevel and local time-stepping discontinuous Galerkin methods for magma dynamics

A high‐order numerical study of reactive dissolution in an upwelling heterogeneous mantle: 2. Effect of shear deformation

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