A Multiscale Model of Partial Melts 1: Effective Equations
Geophysics
2015-05-13 v2 Pattern Formation and Solitons
Abstract
In this paper a model for partial melts is constructed using two-scale homogenization theory. While this technique is well known to the mathematics and materials communities, it is relatively novel to problems in the solid Earth. This approach begins with a grain scale model of the medium, coarsening it into a macroscopic one. The emergent model is in good agreement with previous work, including D. McKenzie's, and serves as verification. This methodology also yields a series of Stokes problems whose solutions provide constitutive relations for permeability and viscosity. A numerical investigation of these relations appears in a companion paper.
Cite
@article{arxiv.0903.0162,
title = {A Multiscale Model of Partial Melts 1: Effective Equations},
author = {Gideon Simpson and Marc Spiegelman and Michael I. Weinstein},
journal= {arXiv preprint arXiv:0903.0162},
year = {2015}
}
Comments
55 pages. Submitted to JGR Solid Earth