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A Multiscale Model of Partial Melts 2: Numerical Results
arXiv.org, v 115(B4), pn/a
04 Sep 2009
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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.
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Details
- Title
- A Multiscale Model of Partial Melts 2: Numerical Results
- Creators
- Gideon SimpsonMarc SpiegelmanMichael Weinstein
- Publication Details
- arXiv.org, v 115(B4), pn/a
- Publisher
- Cornell University Library, arXiv.org; Ithaca
- Resource Type
- Other
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000277264700002
- Scopus ID
- 2-s2.0-78650577551
- Other Identifier
- 991019296792404721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Geochemistry & Geophysics