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High Order Finite Element Solution of Elastohydrodynamic Lubrication Problems

Lu, Hongqiang (2006) High Order Finite Element Solution of Elastohydrodynamic Lubrication Problems. PhD thesis, University of Leeds.

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Abstract

In this thesis, a high-order finite element scheme, based upon the Discontinuous Galerkin (DG) method, is introduced to solve one- and two-dimensional Elastohydrodynamic Lubrication (EHL) problems (line contact and point contact). This thesis provides an introduction to elastohydrodynamic lubrication, including some history, and a description of the underlying mathematical model which is based upon a thin film approximation and a linear elastic model. Following this, typical nondimensionalizations of the equations are discussed, along with boundary conditions. Two families of problems are considered: line and point contacts. Following a review of existing numerical methods for EHL problems, a different numerical technique, known as the Discontinuous Galerkin method is described. This is motivated by the high accuracy requirement for the numerical simulation of EHL problems. This method is successfully applied to steady-state line contact problems. The free boundary is captured accurately using the moving-grid method and the penalty method respectively. Highly accurate numerical results are obtained at a low expense through the use of h-adaptivity methods based on discontinuity and high-order components respectively. Combined with the Crank-Nicolson method and other implicit schemes for the temporal discretization, highly accurate solutions are also obtained for transient line contact problems using the high order DG method for the spatial discretization. In particular, an extra pressure spike is captured, which is difficult to resolve when using low order schemes for spatial discretization. The extension of this high order DG method to the two-dimensional case (point contact) is straightforward. However, the computation in the two-dimensional case is more expensive due to the extra dimension. Hence p-multigrid is employed to improve the efficiency. Since the free boundary in the two-dimensional case is more complicated, only the penalty method is used to handle the cavitation condition. This thesis is ended with the conclusions and a discussion of future work.

Item Type: Thesis (PhD)
Additional Information: Supplied directly by the School of Computing, University of Leeds.
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)
Identification Number/EthosID: uk.bl.ethos.434225
Depositing User: Dr L G Proll
Date Deposited: 24 Mar 2011 14:12
Last Modified: 07 Mar 2014 11:23
URI: http://etheses.whiterose.ac.uk/id/eprint/1341

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