A note on variational multiscale methods for high-contrast heterogeneous porous media flows with rough source terms
KAUST DepartmentApplied Mathematics and Computational Science Program
Earth Science and Engineering Program
Physical Sciences and Engineering (PSE) Division
Environmental Science and Engineering Program
Numerical Porous Media SRI Center (NumPor)
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AbstractIn this short note, we discuss variational multiscale methods for solving porous media flows in high-contrast heterogeneous media with rough source terms. Our objective is to separate, as much as possible, subgrid effects induced by the media properties from those due to heterogeneous source terms. For this reason, enriched coarse spaces designed for high-contrast multiscale problems are used to represent the effects of heterogeneities of the media. Furthermore, rough source terms are captured via auxiliary correction equations that appear in the formulation of variational multiscale methods . These auxiliary equations are localized and one can use additive or multiplicative constructions for the subgrid corrections as discussed in the current paper. Our preliminary numerical results show that one can capture the effects due to both spatial heterogeneities in the coefficients (such as permeability field) and source terms (e.g., due to singular well terms) in one iteration. We test the cases for both smooth source terms and rough source terms and show that with the multiplicative correction, the numerical approximations are more accurate compared to the additive correction. © 2010 Elsevier Ltd.
SponsorsThis work is partially supported by Award Number KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). YE's research was partially supported by the DOE and NSF (DMS 0934837, DMS0621113, DMS 0724704, DMR-0844082, and DMS 0811180).
JournalAdvances in Water Resources