Documents disponibles écrits par cet auteur

Equation-free/galerkin-free reduced-order modeling of the shallow water equations based on proper orthogonal decomposition / Vahid Esfahanian in Transactions of the ASME . Journal of fluids engineering, Vol. 131 N° 7 (Juillet 2009) 

Public ISBD [article]  in Transactions of the ASME . Journal of fluids engineering > Vol. 131 N° 7 (Juillet 2009) . - 13 p. Titre : Equation-free/galerkin-free reduced-order modeling of the shallow water equations based on proper orthogonal decomposition Type de document : texte imprimé Auteurs : Vahid Esfahanian, Auteur ; Khosro Ashrafi, Auteur Année de publication : 2009 Article en page(s) : 13 p. Note générale : fluids engineering Langues : Anglais (eng) Mots-clés : flow  (dynamics);  equations;  functions;  hydraulic  jump;  modeling Résumé : 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. En ligne : http://fluidsengineering.asmedigitalcollection.asme.org/issue.aspx?journalid=122 [...] [article] Equation-free/galerkin-free reduced-order modeling of the shallow water equations based on proper orthogonal decomposition [texte imprimé] / Vahid Esfahanian, Auteur ; Khosro Ashrafi, Auteur . - 2009 . - 13 p. fluids engineering Langues : Anglais (eng) in Transactions of the ASME . Journal of fluids engineering > Vol. 131 N° 7 (Juillet 2009) . - 13 p. Mots-clés : flow  (dynamics);  equations;  functions;  hydraulic  jump;  modeling Résumé : 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. En ligne : http://fluidsengineering.asmedigitalcollection.asme.org/issue.aspx?journalid=122 [...]