In this paper, two categories of reduced-order modeling (ROM) of the shallow water equations (SWEs) based on the proper orthogonal decomposition (POD) are presented. First, the traditional Galerkin-projection POD/ROM is applied to the one-dimensional (1D) SWEs. The result indicates that although the Galerkin-projection POD/ROM is suitable for describing the physical properties of flows (during the POD basis functions’ construction time), it cannot predict that the dynamics of the shallow water flows properly as it was expected, especially with complex initial conditions. Then, the study is extended to applying the equation-free/Galerkin-free POD/ROM to both 1D and 2D SWEs. In the equation-free/Galerkin-free framework, the numerical simulation switches between a fine-scale model, which provides data for construction of the POD basis functions, and a coarse-scale model, which is designed for the coarse-grained computational study of complex, multiscale problems like SWEs. In the present work, the Beam & Warming and semi-implicit time integration schemes are applied to the 1D and 2D SWEs, respectively, as fine-scale models and the coefficients of a few POD basis functions (reduced-order model) are considered as a coarse-scale model. Projective integration is applied to the coarse-scale model in an equation-free framework with a time step grater than the one used for a fine-scale model. It is demonstrated that equation-free/Galerkin-free POD/ROM can resolve the dynamics of the complex shallow water flows. Moreover, the computational cost of the approach is less than the one for a fine-scale model.
Skip Nav Destination
e-mail: evahid@ut.ac.ir
e-mail: khashrafi@ut.ac.ir
Article navigation
July 2009
Research Papers
Equation-Free/Galerkin-Free Reduced-Order Modeling of the Shallow Water Equations Based on Proper Orthogonal Decomposition
Vahid Esfahanian,
Vahid Esfahanian
Department of Mechanical Engineering,
e-mail: evahid@ut.ac.ir
University of Tehran
, North Kargar Avenue, Tehran 11365-4565, Iran
Search for other works by this author on:
Khosro Ashrafi
Khosro Ashrafi
Faculty of Environment,
e-mail: khashrafi@ut.ac.ir
University of Tehran
, Enghelab Avenue, Tehran 14155-6135, Iran
Search for other works by this author on:
Vahid Esfahanian
Department of Mechanical Engineering,
University of Tehran
, North Kargar Avenue, Tehran 11365-4565, Irane-mail: evahid@ut.ac.ir
Khosro Ashrafi
Faculty of Environment,
University of Tehran
, Enghelab Avenue, Tehran 14155-6135, Irane-mail: khashrafi@ut.ac.ir
J. Fluids Eng. Jul 2009, 131(7): 071401 (13 pages)
Published Online: June 23, 2009
Article history
Received:
March 1, 2008
Revised:
April 16, 2009
Published:
June 23, 2009
Citation
Esfahanian, V., and Ashrafi, K. (June 23, 2009). "Equation-Free/Galerkin-Free Reduced-Order Modeling of the Shallow Water Equations Based on Proper Orthogonal Decomposition." ASME. J. Fluids Eng. July 2009; 131(7): 071401. https://doi.org/10.1115/1.3153368
Download citation file:
Get Email Alerts
Related Articles
Simulation of Shallow Flows in Nonuniform Open Channels
J. Fluids Eng (January,2008)
Analysis of Thin Film Flows Using a Flux Vector Splitting
J. Fluids Eng (March,2003)
Numerical Simulation and Evaluation of Velocity Fluctuations During Rotating Stall of a Centrifugal Pump
J. Fluids Eng (August,2011)
Heat Transport by Inverse-Piezoelectric Driven Dream
Pipe
J. Heat Transfer (October,2011)
Related Proceedings Papers
Related Chapters
Physical Properties in the Persian Gulf
Proceedings of the 2010 International Conference on Mechanical, Industrial, and Manufacturing Technologies (MIMT 2010)
Introduction
Introduction to Finite Element, Boundary Element, and Meshless Methods: With Applications to Heat Transfer and Fluid Flow
Computational Modeling of Dynamic Planing Forces
Proceedings of the 10th International Symposium on Cavitation (CAV2018)