An efficient reduced-order method with PGD for solving journal bearing hydrodynamic lubrication problems - 12/10/16

Doi : 10.1016/j.crme.2016.05.006

Bilal Cherabi ^a,^{^⁎} , Abderrachid Hamrani ^a, Idir Belaidi ^a, Sofiane Khelladi ^b, Farid Bakir ^b
^a Research team MISP, LEMI, Université M'hamed-Bougara Boumerdès (UMBB), 35000, Boumerdès, Algeria
^b Arts et Métiers ParisTech, DynFluid, 151, boulevard de l'Hôpital, 75013 Paris, France

^⁎Corresponding author.

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Abstract

In the present work, a reduced-order method, “Proper Generalized Decomposition (PGD)” is extended and applied to the resolution of the Reynolds equation describing the behavior of the lubricant in hydrodynamic journal bearing. The PGD model is employed to solve the characteristic ‘Reynolds’ partial differential equation using the separation technique through the alternating direction strategy. The resulting separated-dimension system has a low computation cost compared to classical finite-difference resolution. Several numerical benchmark examples are investigated to verify the validity and accuracy of the proposed method. It has been found that numerical results obtained by the PGD method can achieve an improved convergence rate with a very low computation cost.

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Keywords : Hydrodynamic journal bearing, Reynolds equation, Reduced order modeling, Proper Generalized Decomposition