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Flux formulation of parabolic equations with highly heterogeneous coefficients
Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada..
KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
Russian Acad Sci, Nucl Safety Inst, 52 B Tulskaya, Moscow, Russia.;North Eastern Fed Univ, 58 Belinskogo, Yakutsk, Russia..
2018 (English)In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 340, p. 582-601Article in journal (Refereed) Published
Abstract [en]

In this paper we study the flux formulation of unsteady diffusion equations with highly heterogeneous permeability coefficients and their discretization. In the proposed approach first an equation governing the flux of the unknown scalar quantity is solved, and then the scalar is recovered from its flux. The problem for the flux is further discretized by splitting schemes that yield locally one-dimensional problems, and therefore, the resulting linear systems are tridiagonal if the spatial discretization uses Cartesian grids. A first and a formally second order time discretization splitting scheme have been implemented in both two and three dimensions, and we present results for a few model problems using a challenging benchmark dataset.

Place, publisher, year, edition, pages
Elsevier, 2018. Vol. 340, p. 582-601
Keywords [en]
Direction-splitting, Multi-scale methods, Parabolic equations, Flux-splitting
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-233406DOI: 10.1016/j.cam.2017.12.003ISI: 000440264600039Scopus ID: 2-s2.0-85039852613OAI: oai:DiVA.org:kth-233406DiVA, id: diva2:1240439
Note

QC 20180821

Available from: 2018-08-21 Created: 2018-08-21 Last updated: 2018-08-21Bibliographically approved

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Srinivasan, Shriram
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