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Title: A Three‐Field Formulation for Two‐Phase Flow in Geodynamic Modeling: Toward the Zero‐Porosity Limit
Abstract

Two‐phase flow, a system where Stokes flow and Darcy flow are coupled, is of great importance in the Earth's interior, such as in subduction zones, mid‐ocean ridges, and hotspots. However, it remains challenging to solve the two‐phase equations accurately in the zero‐porosity limit, for example, when melt is fully frozen below solidus temperature. Here we propose a new three‐field formulation of the two‐phase system, with solid velocity (vs), total pressure (Pt), and fluid pressure (Pf) as unknowns, and present a robust finite‐element implementation, which can be used to solve problems in which domains of both zero porosity and non‐zero porosity are present. The reformulated equations include regularization to avoid singularities and exactly recover to the standard single‐phase incompressible Stokes problem at zero porosity. We verify the correctness of our implementation using the method of manufactured solutions and analytic solutions and demonstrate that we can obtain the expected convergence rates in both space and time. Example experiments, such as self‐compaction, falling block, and mid‐ocean ridge spreading show that this formulation can robustly resolve zero‐ and non‐zero‐porosity domains simultaneously, and can be used for a large range of applications in various geodynamic settings.

 
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Award ID(s):
2121568
NSF-PAR ID:
10484097
Author(s) / Creator(s):
 ;  ;  
Publisher / Repository:
DOI PREFIX: 10.1029
Date Published:
Journal Name:
Journal of Geophysical Research: Solid Earth
Volume:
129
Issue:
1
ISSN:
2169-9313
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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