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Using empirical Eigenfunctions and Galerkin method to two-phase transport models

✍ Scribed by Abdollah Shidfar; Masoumeh Mohammadi

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
444 KB
Volume
23
Category
Article
ISSN
0749-159X

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✦ Synopsis

Abstract

In this article, we consider a nonlinear partial differential system describing two‐phase transports and try to recover the source term and the nonlinear diffusion term when the state variable is known at different profile times. To this end, we use a POD‐Galerkin procedure in which the proper orthogonal decomposition technique is applied to the ensemble of solutions to derive empirical eigenfunctions. These empirical eigenfunctions are then used as basis functions within a Galerkin method to transform the partial differential equation into a set of ordinary differential equations. Finally, the validation of the used method has been evaluated by some numerical examples. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 456–474, 2007

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