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Lubricants 2018, 6(4), 95; https://doi.org/10.3390/lubricants6040095

Accuracy and Grid Convergence of the Numerical Solution of the Energy Equation in Fluid Film Lubrication: Application to the 1D Slider

1
ERMES-IMSIA, EDF Lab Paris-Saclay, 91120 Palaiseau, France
2
Institut Pprime, UPR CNRS 3346, Université de Poitiers, ISAE ENSMA, 86962 Chasseneuil Futuroscope, France
*
Author to whom correspondence should be addressed.
Received: 13 September 2018 / Revised: 19 October 2018 / Accepted: 22 October 2018 / Published: 26 October 2018
(This article belongs to the Special Issue Fluid-Film Lubrication)
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Abstract

The present work is focused on the numerical solution of the complete energy equation used in fluid film lubrication. The work was motivated by the fact that the complete energy equation has no analytical solution that can be used for validations. Its accuracy and computation time are related to the employed numerical method and to the grid resolution. The natural discretization method (NDM) applied on different grids is systematically compared with the spectral method (the Lobatto Point Colocation Method or LPCM) with different polynomial degrees. A one dimensional inclined slider is used for the numerical tests, and the energy equation is artificially decoupled from the Reynolds equation. This approach enables us to focus all the attention on the numerical solution of the energy equation. The results show that the LPCM is one or two orders of magnitude more efficient than the NDM in terms of computation time. The energy equation is then coupled with the Reynolds equation in a thermo-hydrodynamic analysis of the same 1D slider; the numerical results confirm again the efficiency of the LPCM. A thermo-hydrodynamic analysis of a two-lobe journal bearing is then presented as a practical application. View Full-Text
Keywords: energy equation; numerical solution; lobatto point quadrature; legendre polynomials energy equation; numerical solution; lobatto point quadrature; legendre polynomials
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Zhang, S.; Hassini, M.-A.; Arghir, M. Accuracy and Grid Convergence of the Numerical Solution of the Energy Equation in Fluid Film Lubrication: Application to the 1D Slider. Lubricants 2018, 6, 95.

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