SAM
https://sam.ensam.eu:443
The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Wed, 17 Jul 2024 11:15:00 GMT2024-07-17T11:15:00ZSimulation of Heat and Mass Transport in a Square Lid-Driven Cavity with Proper Generalized Decomposition (PGD)
http://hdl.handle.net/10985/10267
Simulation of Heat and Mass Transport in a Square Lid-Driven Cavity with Proper Generalized Decomposition (PGD)
DUMON, Antoine; ALLERY, Cyrille; AMMAR, Amine
The aim of this study is to apply proper generalized decomposition (PGD) to solve mixed-convection problems with and without mass transport in a two dimensional lid-driven cavity. PGD is an iterative reduced order model approach which consists of solving a partial differential equation while seeking the solution in separated form. Comparisons with results in the literature and with results from a standard solver are make. For the case of a mixed-convection problem without mass transfer, three Richardson numbers are considered, Ri=0.1, Ri=1, and Ri=10. In this case, PGD is seven times faster than the standard solver with Ri=10 with a similar accuracy. For the case with mass transfer, simulations are done with different Lewis numbers, Le=5, Le=25, and Le=50, and with different value of the ratio N between the solutal and the thermal Grashoff numbers. In this case, too, PGD is ten times faster than the standard solver.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/102672013-01-01T00:00:00ZDUMON, AntoineALLERY, CyrilleAMMAR, AmineThe aim of this study is to apply proper generalized decomposition (PGD) to solve mixed-convection problems with and without mass transport in a two dimensional lid-driven cavity. PGD is an iterative reduced order model approach which consists of solving a partial differential equation while seeking the solution in separated form. Comparisons with results in the literature and with results from a standard solver are make. For the case of a mixed-convection problem without mass transfer, three Richardson numbers are considered, Ri=0.1, Ri=1, and Ri=10. In this case, PGD is seven times faster than the standard solver with Ri=10 with a similar accuracy. For the case with mass transfer, simulations are done with different Lewis numbers, Le=5, Le=25, and Le=50, and with different value of the ratio N between the solutal and the thermal Grashoff numbers. In this case, too, PGD is ten times faster than the standard solver.Proper general decomposition (PGD) for the resolution of Navier–Stokes equations
http://hdl.handle.net/10985/8469
Proper general decomposition (PGD) for the resolution of Navier–Stokes equations
DUMON, Antoine; ALLERY, Cyrille; AMMAR, Amine
In this work, the PGD method will be considered for solving some problems of fluid mechanics by looking for the solution as a sum of tensor product functions. In the first stage, the equations of Stokes and Burgers will be solved. Then, we will solve the Navier–Stokes problem in the case of the lid-driven cavity for different Reynolds numbers (Re = 100, 1000 and 10,000). Finally, the PGD method will be compared to the standard resolution technique, both in terms of CPU time and accuracy.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10985/84692011-01-01T00:00:00ZDUMON, AntoineALLERY, CyrilleAMMAR, AmineIn this work, the PGD method will be considered for solving some problems of fluid mechanics by looking for the solution as a sum of tensor product functions. In the first stage, the equations of Stokes and Burgers will be solved. Then, we will solve the Navier–Stokes problem in the case of the lid-driven cavity for different Reynolds numbers (Re = 100, 1000 and 10,000). Finally, the PGD method will be compared to the standard resolution technique, both in terms of CPU time and accuracy.Proper Generalized Decomposition method for incompressible Navier–Stokes equations with a spectral discretization
http://hdl.handle.net/10985/8487
Proper Generalized Decomposition method for incompressible Navier–Stokes equations with a spectral discretization
DUMON, Antoine; ALLERY, Cyrille; AMMAR, Amine
Proper Generalized Decomposition (PGD) is a method which consists in looking for the solution to a problem in a separate form. This approach has been increasingly used over the last few years to solve mathematical problems. The originality of this work consists in the association of PGD with a spectral collocation method to solve transfer equations as well as Navier–Stokes equations. In the first stage, the PGD method and its association with spectral discretization is detailed. This approach was tested for several problems: the Poisson equation, the Darcy problem, Navier–Stokes equations (the Taylor Green problem and the lid-driven cavity). In the Navier–Stokes problems, the coupling between velocity and pressure was performed using a fractional step scheme and a PN—PN-2 discretization. For all problems considered, the results from PGD simulations were compared with those obtained by a standard solver and/or with the results found in the literature. The simulations performed showed that PGD is as accurate as standard solvers. PGD preserves the spectral behavior of the errors in velocity and pressure when the time step or the space step decreases. Moreover, for a given number of discretization nodes, PGD is faster than the standard solvers.
http://dx.doi.org/10.1016/j.amc.2013.02.022
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/84872013-01-01T00:00:00ZDUMON, AntoineALLERY, CyrilleAMMAR, AmineProper Generalized Decomposition (PGD) is a method which consists in looking for the solution to a problem in a separate form. This approach has been increasingly used over the last few years to solve mathematical problems. The originality of this work consists in the association of PGD with a spectral collocation method to solve transfer equations as well as Navier–Stokes equations. In the first stage, the PGD method and its association with spectral discretization is detailed. This approach was tested for several problems: the Poisson equation, the Darcy problem, Navier–Stokes equations (the Taylor Green problem and the lid-driven cavity). In the Navier–Stokes problems, the coupling between velocity and pressure was performed using a fractional step scheme and a PN—PN-2 discretization. For all problems considered, the results from PGD simulations were compared with those obtained by a standard solver and/or with the results found in the literature. The simulations performed showed that PGD is as accurate as standard solvers. PGD preserves the spectral behavior of the errors in velocity and pressure when the time step or the space step decreases. Moreover, for a given number of discretization nodes, PGD is faster than the standard solvers.