A new formulation for coupled magma/mantle dynamics. Issue 1 (17th May 2019)

• Record Type: Journal Article
• Authors: Dannberg, Juliane; Gassmöller, Rene; Grove, Ryan; Heister, Timo
• Is Part Of: Geophysical journal international. Volume 219:Issue 1(2019)
• Page Start: 94
• Page End: 107
• Publication Date: 2019-05-17
• Subjects: Numerical solutions -- Dynamics of lithosphere and mantle -- Mechanics, theory, and modelling -- Mid-ocean ridge processes -- Magma migration and fragmentation; Geophysics -- Periodicals; 550
• DOI: 10.1093/gji/ggz190
• Languages: English
• ISSNs: 0956-540X

Abstract

SUMMARY: Modelling the porous flow of melt through a viscously deforming solid rock matrix is a useful tool for interpreting observations from the Earth's surface, and advances our understanding of the dynamics of the Earth's interior. However, the system of equations describing this process becomes mathematically degenerate in the limit of vanishing melt fraction. Numerical methods that do not consider this degeneracy or avoid it solely by regularizing specific material properties generally become computationally expensive as soon as the melt fraction approaches zero in some part of the domain. Here, we present a new formulation of the equations for coupled magma/mantle dynamics that addresses this problem, and allows it to accurately compute large-scale 3-D magma/mantle dynamics simulations with extensive regions of zero melt fraction. We achieve this by rescaling one of the solution variables, the compaction pressure, which ensures that for vanishing melt fraction, the equation causing the degeneracy becomes an identity and the other two equations revert to the Stokes system. This allows us to split the domain into two parts: in mesh cells where melt is present, we solve the coupled system of magma/mantle dynamics. In cells without melt, we solve the Stokes system as it is done for mantle convection without melt transport and constrain the remaining degrees of freedom. We have implemented this formulation in the open source geodynamic modelling codeAspect and illustrate the improved performance compared to the previous three-field formulation, showing numerically that the new formulation is robust in terms of problem size and only slightly sensitive to model parameters. Beyond that, we demonstrate the applicability to realistic problems by showing large-scale 2-D and 3-D models of mid-ocean ridges with complex rheology. Hence, we believe that our new formulation and its implementation inAspect will prove a valuable tool for studying the interaction of melt segregating through and interacting with a solid host rock in the Earth and other planetary bodies using high-resolution, 3-D simulations.