Application of POD and DEIM to Dimension Reduction of Nonlinear Miscible Viscous Fingering in Porous Media

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dc.contributor.authorChaturantabut, Saifon
dc.contributor.authorSorensen, Danny C.
dc.date.accessioned2018-06-19T17:45:08Z
dc.date.available2018-06-19T17:45:08Z
dc.date.issued2009-07
dc.date.noteJuly 2009
dc.description.abstractA Discrete Empirical Interpolation Method (DEIM) is applied in conjunction with Proper Orthogonal Decomposition (POD) to construct a nonlinear reduced-order model of finite difference discretized system used in the simulation of nonlinear miscible viscous fingering in a 2-D porous medium. POD is first applied to extract a low-dimensional basis that optimally captures the dominant characteristics of the system trajectory. This basis is then used in a Galerkin projection scheme to construct a reduced-order system. DEIM is then applied to greatly improve the efficiency in computing the projected nonlinear terms in the POD reduced system. DEIM achieves a complexity reduction of the nonlinearities which is proportional to the number of reduced variables while POD retains a complexity proportional to the original number of variables. Numerical results demonstrate that the dynamics of the viscous fingering in the full-order system of dimension 15000 can be captured accurately by the POD-DEIM reduced system of dimension 40 with the computational time reduced by factor of O(1000).
dc.format.extent26 pp
dc.identifier.citationChaturantabut, Saifon and Sorensen, Danny C.. "Application of POD and DEIM to Dimension Reduction of Nonlinear Miscible Viscous Fingering in Porous Media." (2009) <a href="https://hdl.handle.net/1911/102127">https://hdl.handle.net/1911/102127</a>.
dc.identifier.digitalTR09-25
dc.identifier.urihttps://hdl.handle.net/1911/102127
dc.language.isoeng
dc.titleApplication of POD and DEIM to Dimension Reduction of Nonlinear Miscible Viscous Fingering in Porous Media
dc.typeTechnical report
dc.type.dcmiText
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