Visco-plastic models of magma dynamics using FD-PDE: a PETSc-based, finite-difference staggered-grid framework for solving partial differential equations
Abstract
The role of magmatism in the tectonic force balance at divergent plate boundaries remains unclear. In the RIFT-O-MAT project, we seek to understand how magmatism promotes and shapes rifts in continental and oceanic lithosphere by using models that build upon the two-phase flow theory of magma/rock interaction. A key challenge is to extend the magma dynamics theory to account for the non-linear rheological behaviour of the host rocks, and investigate processes such as diking or faulting.
Failure of rocks (plasticity) is an essential ingredient in geodynamics models as Earth materials cannot sustain unbounded stresses. However, plasticity represents a non-trivial problem even for single-phase flow formulations (Spiegelman et al. 2016). Furthermore, there are few poro-visco-plastic approaches within the geodynamic modelling community. Many questions remain as to appropriate models of plasticity as well as effective solvers for these strongly nonlinear systems. We built a new finite difference staggered grid framework for solving partial differential equations (FD-PDE) for single-/two-phase flow magma dynamics (Pusok et al., 2020). Staggered grid finite-difference methods are mimetic, conservative, inf-sup stable and with small stencil — thus they are well suited to address these problems. The FD-PDE framework uses PETSc (Balay et al., 2020) and aims to separate the user input from the discretization of governing equations. The core goals for the FD-PDE framework is to allow for extensible development, and implement a robust framework for testing. Here, we present several simplified model problems with our new FD-PDE framework for two-phase flow visco-plastic models designed to elucidate numerical issues and propose solutions for these formulations. Balay et al. (2020), PETSc Users Manual, ANL-95/11 - Revision 3.13. Pusok et al. (2020) https://doi.org/10.5194/egusphere-egu2020-18690 Spiegelman et al. (2016) https://doi.org/10.1002/2015GC006228- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2020
- Bibcode:
- 2020AGUFMDI0070007P
- Keywords:
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- 3619 Magma genesis and partial melting;
- MINERALOGY AND PETROLOGY;
- 8145 Physics of magma and magma bodies;
- TECTONOPHYSICS;
- 8148 Planetary volcanism;
- TECTONOPHYSICS;
- 8178 Tectonics and magmatism;
- TECTONOPHYSICS