A high order spectral volume method for elastohydrodynamic lubrication problems: Formulation and application of an implicit p-multigrid algorithm for line contact problems

2011 ◽  
Vol 48 (1) ◽  
pp. 44-53 ◽  
Author(s):  
R. Kannan
Keyword(s):  
Elastohydrodynamic Lubrication ◽  
Contact Problems ◽  
High Order ◽  
Line Contact ◽  
Multigrid Algorithm ◽  
Spectral Volume ◽  
Volume Method

Fully Coupled Numerical Methods for Elastohydrodynamic Lubrication Line Contact Problems by the High Order Finite Difference Methods

2021 ◽  
Author(s):  
QUAN SHEN ◽  
Bing Wu ◽  
GUANGWEN XIAO
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Scheme ◽  
Difference Method ◽  
Elastohydrodynamic Lubrication ◽  
Contact Problems ◽  
High Order ◽  
Line Contact ◽  
High Order Finite Difference ◽  
Upwind Finite Difference

Abstract In this paper a high order finite difference method is constructed to solve the elastohydrodynamic lubrication line contact problems, whose cavitation condition is handled by the penalty method. The highly nonlinear equations from the discretization of the high order finite difference method are solved by the trust-region dogleg algorithm. In order to reduce the numerical dissipation and dispersion brought by the high order upwind finite difference scheme, a high order biased upwind finite difference scheme is also presented. Our method is found to achieve more accurate solutions using just a small number of nodes compared to the multilevel methods combined with the lower order finite difference method.

Higher Resolution Hybrid-Upwind Spectral Finite-Volume Methods, for Flow in Porous and Fractured Media on Unstructured Grids

2021 ◽  
Author(s):  
Yawei Xie ◽  
Michael G. Edwards
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Unstructured Grids ◽  
Concentration Field ◽  
Convective Transport ◽  
High Order ◽  
Spectral Volume ◽  
Flux Approximation ◽  
Triangular Cell ◽  
Volume Method

Abstract A novel higher resolution spectral volume method coupled with a control-volume distributed multi-Point flux approximation (CVD-MPFA) is presented on unstructured triangular grids for subsurface reservoir simulation. The flow equations involve an essentially hyperbolic convection equation coupled with an elliptic pressure equation resulting from Darcy’s law together with mass conservation. The spectral volume (SV) method is a locally conservative, efficient high-order finite volume method for convective flow. In 2D geometry, the triangular cell is subdivided into sub-cells, and the average state variables in the sub-cells are used to reconstruct a high-order polynomial in the triangular cell. The focus here is on an efficient strategy for reconstruction of both a higher resolution approximation of the convective transport flux and Darcy-flux approximation on sub-cell interfaces, which is also coupled with a discrete fracture model. The strategy involves coupling of the SV method and reconstructed CVD-MPFA fluxes at the faces of the spectral volume, to obtain an efficient finer scale higher resolution finite-volume method which solves for both the saturation and pressure. A limiting procedure based on a Barth-Jespersen type limiter is used to prevent non-physical oscillations on unstructured grids. The fine scale saturation/concentration field is then updated via the reconstructed finite volume approximation over the sub-cell control-volumes. Performance comparisons are presented for two phase flow problems on 2D unstructured meshes including fractures. The results demonstrate that the spectral-volume method achieves further enhanced resolution of flow and fronts in addition to that of achieved by the standard higher resolution method over first order upwind, while improving upon efficiency.

Thermal Effects in an Elastohydrodynamic Line Contact Using a CFD Approach

2007 ◽  
Author(s):  
Markus Hartinger ◽  
David Gosman ◽  
Stathis Ioannides ◽  
Hugh Spikes
Keyword(s):  
Thermal Effects ◽  
Elastohydrodynamic Lubrication ◽  
Rolling Element Bearing ◽  
Line Contact ◽  
Rolling Element ◽  
Model Fluid ◽  
Element Bearing ◽  
Effects Of Temperature ◽  
Fluid Behaviour ◽  
Volume Method

Traditionally the problem of elastohydrodynamic lubrication (EHL) has been solved using the Reynolds equations for fluid flow. In this paper we explore the finite volume method (FVM) to model fluid behaviour in rolling-element bearing systems. We discuss the effects of temperature in an ehl line contact, which results in a non-uniform viscosity distribution across the film. Furthermore, the thermodynamic implications of using a Reynolds-condition like cavitation model are investigated.

Effect of Roughness Orientation on the Elastohydrodynamic Lubrication Film Thickness

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Dong Zhu ◽  
Q. Jane Wang
Keyword(s):  
Film Thickness ◽  
Stochastic Models ◽  
Deterministic Model ◽  
Elastohydrodynamic Lubrication ◽  
Contact Problems ◽  
Operating Conditions ◽  
Orientation Effect ◽  
Line Contact ◽  
Lubrication Film ◽  
Dry Contact

Effect of roughness orientation on lubricant film thickness has been an important issue of surface design, attracting much attention since the 1970 s. A systematical study, however, is still needed for various contact types in an extended range of operating conditions, especially in mixed lubrication cases with film thickness to roughness ratio (λ ratio) smaller than 0.5. The present study employs a deterministic mixed elastohydrodynamic lubrication (EHL) model to investigate the performance of lubricating films in different types of contact geometry, including the line contact, circular contact, and elliptical contacts of various ellipticity ratios. The speed range for analyzed cases covers 11 orders of magnitude so that the entire transition from full-film and mixed EHL down to dry contact (corresponding λ ratio from about 3.5 down to 0.001 or so) is simulated. Three types of machined surfaces are used, representing transverse, longitudinal, and isotropic roughness, respectively. The line contact results are compared with those from the stochastic models by Patir and Cheng (“Effect of Surface Roughness Orientation on the Central Film Thickness in EHD Contacts,” Proc. 5th Leeds-Lyon Symp. on Tribol., 1978, pp. 15–21) and the influence of roughness orientation predicted by the deterministic model is found to be less significant than that by the stochastic models, although the basic trends are about the same when λ > 0.5. The orientation effect for circular or elliptical contact problems appears to be more complicated than that for line contacts due to the existence of significant lateral flows. In circular contacts, or elliptical contacts with the ellipticity ratio smaller than one, the longitudinal roughness may become more favorable than the isotropic and transverse. Overall, the orientation effect is significant in the mixed EHL regime where theλratio is roughly in the range from 0.05 to 1.0. It is relatively insignificant for both the full-film EHL (λ > 1.2 or so) and the boundary lubrication/dry contact (λ < 0.025 ∼ 0.05).

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