A Multiscale Model of Partial Melts 2: Numerical Results

Abstract

In a companion paper, equations for partially molten media were derived using two-scale homogenization theory. One advantage of homogenization is that material properties, such as permeability and viscosity, readily emerge. A caveat is that the dependence of these parameters upon the microstructure is not self-evident. In particular, one seeks to relate them to the porosity. In this paper, we numerically solve ensembles of the cell problems from which these quantities emerge. Using this data, we estimate relationships between the parameters and the porosity. In particular, the bulk viscosity appears to be inversely proportional to the porosity. Finally, we synthesize these numerical estimates with the models. Our hybrid numerical--analytical model predicts that the compaction length vanishes with porosity.

50 pages, submitted to JGR Solid Earth

References in corpus (3)

• A compiler for variational forms
• A Multiscale Model of Partial Melts 1: Effective Equations
• Efficient Compilation of a Class of Variational Forms

Cited by in corpus (7)

• A Multiscale Model of Partial Melts 1: Effective Equations
• The viscosities of partially molten materials undergoing diffusion creep
• Melt-preferred orientation, anisotropic permeability, and melt-band formation in a deforming, partially molten aggregate
• Analysis of block-preconditioners for models of coupled magma/mantle dynamics
• Magmatic channelisation by reactive and shear-driven instabilities at mid-ocean ridges: a combined analysis
• Torsion of a cylinder of partially molten rock with a spherical inclusion: theory and simulation
• Existence theory for magma equations in dimension two and higher