Dimensional reduction of type PGD for solving incompressible flows
type: Dataset
description: Motivated by solving the Navier-Stokes equations, this work presents the implementation and development of a reduced order model, the PGD (Proper Generalized Decomposition).Firstly, this method is applied to solving equations models with an analytical solution. The stationary diffusion equation 2D and 3D, 2D unsteady diffusion equation and Burgers equations and Stokes are processed. We show that in all these cases, the PGD method allows to find analytical solutions with a good accuracy compared to the standard model. We also demonstrate the superiority of the PGD relative to the standard model in terms of computing time. Indeed, in all these cases, PGD was much more rapid than the standard solver (several dozen times). The Navier-Stokes 2D and 3D thermal and isothermal isotherms are then processed by a finite volume discretization on a staggered grid where the velocity-pressure coupling was handled using a prediction-correction scheme. In this case a decomposition of the space variables only was chosen. The results in 2D for Reynolds numbers equal to 100, 1000and 10, 000 are similar to those of the solver standard with a significant time saving (PGD isten times faster than the solver standard). Finally, this work introduces a first approach tosolving the Navier-Stokes equations with a spectral method coupled with the PGD. Different cases were dealed, the stationary diffusion equation, the Darcy equation and the Navier-Sokesequations. PGD showed a good accuracy compared with the standard solver. Saving time was observed for the case of the Poisson equation, on the other hand, about Darcy’s problem or Navier-Stokes’ equations, performance of the PGD in terms of computing time may yet be improved.
identifier: NNT: 2011LAROS327
issued: 2026-05-21T19:47:24.889088
language: fr
modified: 2026-05-21T19:47:24.889102
contact point: Organization
  fn: CCSD
keyword: computational-fluid-mechanics
keyword: ecoulements-isothermesanisothermes
keyword: flow-insulatedisothermal
keyword: formulation-spectrale
keyword: infoeu-reposemanticsdoctoralthesis
keyword: mecanique-des-fluides-numerique
keyword: proper-generalized-decomposition-pgd
keyword: reduced-order-models-rom
keyword: reduction-de-modeles-rom
keyword: separation-de-variables
keyword: separation-of-variables
keyword: spectral-formuation
keyword: spiotherengineering-sciences-physicsother
keyword: theses
landing page: https://theses.hal.science/tel-00644565

Dimensional reduction of type PGD for solving incompressible flows
type: Distribution
format: HTML
issued: 2026-05-21T19:47:24.904401
modified: 2026-05-21T19:47:24.835387
access URL: https://theses.hal.science/tel-00644565

test_moissonnage_selune
type: Agent