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Application of POD and DEIM on dimension reduction of non-linear miscible viscous fingering in porous media

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  • Saifon Chaturantabut
  • Danny C. Sorensen

Abstract

A discrete empirical interpolation method (DEIM) is applied in conjunction with proper orthogonal decomposition (POD) to construct a non-linear reduced-order model of a finite difference discretized system used in the simulation of non-linear 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 non-linear terms in the POD reduced system. DEIM achieves a complexity reduction of the non-linearities, which is proportional to the number of reduced variables, whereas 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 15,000 can be captured accurately by the POD--DEIM reduced system of dimension 40 with the computational time reduced by factor of .

Suggested Citation

  • Saifon Chaturantabut & Danny C. Sorensen, 2010. "Application of POD and DEIM on dimension reduction of non-linear miscible viscous fingering in porous media," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 17(4), pages 337-353, July.
    • Handle: RePEc:taf:nmcmxx:v:17:y:2010:i:4:p:337-353
    DOI: 10.1080/13873954.2011.547660
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    References listed on IDEAS

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    1. K. Kunisch & S. Volkwein, 1999. "Control of the Burgers Equation by a Reduced-Order Approach Using Proper Orthogonal Decomposition," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 345-371, August.
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