A reduced-order finite volume element formulation based on POD method and numerical simulation for two-dimensional solute transport problems

Zhendong Luo, Hong Li, Ping Sun, Jing An and Ionel Michael Navon

Mathematics and Computers in Simulation (MATCOM), 2013, vol. 89, issue C, 50-68

Abstract: Proper orthogonal decomposition (POD) method has been successfully used in the reduced-order modeling of complex systems. In this paper, we extend the applications of POD method, i.e., combine the classical finite volume element (FVE) method with the POD method to obtain a reduced-order FVE formulation with lower dimensions and sufficiently high accuracy for two-dimensional solute transport problems, which have real life practical applications. We then provide error estimates between the reduced-order POD FVE solutions and classical FVE solutions and we provide implementation of an extrapolation algorithm for solving the reduced-order FVE formulation. Thus, we provide the theoretical basis for practical applications. A numerical example is then used to ascertain that the results of numerical computation are consistent with the theoretical derivations. Moreover, it is shown that the reduced-order FVE formulation based on POD method is both feasible and efficient for solving two-dimensional solute transport problems.

Keywords: Proper orthogonal decomposition; Finite volume element formulation; Error estimate; Two-dimensional solute transport problems; Numerical simulation (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:89:y:2013:i:c:p:50-68

DOI: 10.1016/j.matcom.2012.11.012

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