Volume 30, Issue 1
A Novel Iterative Penalty Method to Enforce Boundary Conditions in Finite Volume POD-Galerkin Reduced Order Models for Fluid Dynamics Problems

S. Kelbij Star, Giovanni Stabile, Francesco Belloni, Gianluigi Rozza & Joris Degroote

Commun. Comput. Phys., 30 (2021), pp. 34-66.

Published online: 2021-04

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  • Abstract

A Finite-Volume based POD-Galerkin reduced order model is developed for fluid dynamics problems where the (time-dependent) boundary conditions are controlled using two different boundary control strategies: the lifting function method, whose aim is to obtain homogeneous basis functions for the reduced basis space and the penalty method where the boundary conditions are enforced in the reduced order model using a penalty factor. The penalty method is improved by using an iterative solver for the determination of the penalty factor rather than tuning the factor with a sensitivity analysis or numerical experimentation.
The boundary control methods are compared and tested for two cases: the classical lid driven cavity benchmark problem and a Y-junction flow case with two inlet channels and one outlet channel. The results show that the boundaries of the reduced order model can be controlled with the boundary control methods and the same order of accuracy is achieved for the velocity and pressure fields. Finally, the reduced order models are 270-308 times faster than the full order models for the lid driven cavity test case and 13-24 times for the Y-junction test case.

  • Keywords

Proper Orthogonal Decomposition, Navier–Stokes equations, Galerkin projection, penalty method, lifting function method, iterative method.

  • AMS Subject Headings

35Q25, 65N08, 76M12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-30-34, author = {Star , S. Kelbij and Stabile , Giovanni and Belloni , Francesco and Rozza , Gianluigi and Degroote , Joris}, title = {A Novel Iterative Penalty Method to Enforce Boundary Conditions in Finite Volume POD-Galerkin Reduced Order Models for Fluid Dynamics Problems}, journal = {Communications in Computational Physics}, year = {2021}, volume = {30}, number = {1}, pages = {34--66}, abstract = {

A Finite-Volume based POD-Galerkin reduced order model is developed for fluid dynamics problems where the (time-dependent) boundary conditions are controlled using two different boundary control strategies: the lifting function method, whose aim is to obtain homogeneous basis functions for the reduced basis space and the penalty method where the boundary conditions are enforced in the reduced order model using a penalty factor. The penalty method is improved by using an iterative solver for the determination of the penalty factor rather than tuning the factor with a sensitivity analysis or numerical experimentation.
The boundary control methods are compared and tested for two cases: the classical lid driven cavity benchmark problem and a Y-junction flow case with two inlet channels and one outlet channel. The results show that the boundaries of the reduced order model can be controlled with the boundary control methods and the same order of accuracy is achieved for the velocity and pressure fields. Finally, the reduced order models are 270-308 times faster than the full order models for the lid driven cavity test case and 13-24 times for the Y-junction test case.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0059}, url = {http://global-sci.org/intro/article_detail/cicp/18873.html} }
TY - JOUR T1 - A Novel Iterative Penalty Method to Enforce Boundary Conditions in Finite Volume POD-Galerkin Reduced Order Models for Fluid Dynamics Problems AU - Star , S. Kelbij AU - Stabile , Giovanni AU - Belloni , Francesco AU - Rozza , Gianluigi AU - Degroote , Joris JO - Communications in Computational Physics VL - 1 SP - 34 EP - 66 PY - 2021 DA - 2021/04 SN - 30 DO - http://doi.org/10.4208/cicp.OA-2020-0059 UR - https://global-sci.org/intro/article_detail/cicp/18873.html KW - Proper Orthogonal Decomposition, Navier–Stokes equations, Galerkin projection, penalty method, lifting function method, iterative method. AB -

A Finite-Volume based POD-Galerkin reduced order model is developed for fluid dynamics problems where the (time-dependent) boundary conditions are controlled using two different boundary control strategies: the lifting function method, whose aim is to obtain homogeneous basis functions for the reduced basis space and the penalty method where the boundary conditions are enforced in the reduced order model using a penalty factor. The penalty method is improved by using an iterative solver for the determination of the penalty factor rather than tuning the factor with a sensitivity analysis or numerical experimentation.
The boundary control methods are compared and tested for two cases: the classical lid driven cavity benchmark problem and a Y-junction flow case with two inlet channels and one outlet channel. The results show that the boundaries of the reduced order model can be controlled with the boundary control methods and the same order of accuracy is achieved for the velocity and pressure fields. Finally, the reduced order models are 270-308 times faster than the full order models for the lid driven cavity test case and 13-24 times for the Y-junction test case.

S. Kelbij Star, Giovanni Stabile, Francesco Belloni, Gianluigi Rozza & Joris Degroote. (2021). A Novel Iterative Penalty Method to Enforce Boundary Conditions in Finite Volume POD-Galerkin Reduced Order Models for Fluid Dynamics Problems. Communications in Computational Physics. 30 (1). 34-66. doi:10.4208/cicp.OA-2020-0059
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