scholarly journals Estimates for the Upscaling Error in Heterogeneous Multiscale Methods for Wave Propagation Problems in Locally Periodic Media

2017 ◽  
Vol 15 (2) ◽  
pp. 948-976 ◽  
Author(s):  
Doghonay Arjmand ◽  
Olof Runborg
Keyword(s):  
Wave Propagation ◽  
Multiscale Methods ◽  
Periodic Media ◽  
Heterogeneous Multiscale

scholarly journals On the Two-Scale Modelling of Elastohydrodynamic Lubrication in Tilted-Pad Bearings

Lubricants ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 78 ◽  
Author(s):  
Gregory de Boer ◽  
Andreas Almqvist
Keyword(s):  
Surface Topography ◽  
Load Capacity ◽  
Three Dimensional ◽  
Elastohydrodynamic Lubrication ◽  
Multiscale Methods ◽  
Operating Conditions ◽  
Real Surface ◽  
Micro Scale ◽  
Macro Scale ◽  
Heterogeneous Multiscale

A two-scale method for modelling the Elastohydrodynamic Lubrication (EHL) of tilted-pad bearings is derived and a range of solutions are presented. The method is developed from previous publications and is based on the Heterogeneous Multiscale Methods (HMM). It facilitates, by means of homogenization, incorporating the effects of surface topography in the analysis of tilted-pad bearings. New to this article is the investigation of three-dimensional bearings, including the effects of both ideal and real surface topographies, micro-cavitation, and the metamodeling procedure used in coupling the problem scales. Solutions for smooth bearing surfaces, and under pure hydrodynamic operating conditions, obtained with the present two-scale EHL model, demonstrate equivalence to those obtained from well-established homogenization methods. Solutions obtained for elastohydrodynamic operating conditions, show a dependency of the solution to the pad thickness and load capacity of the bearing. More precisely, the response for the real surface topography was found to be stiffer in comparison to the ideal. Micro-scale results demonstrate periodicity of the flow and surface topography and this is consistent with the requirements of the HMM. The means of selecting micro-scale simulations based on intermediate macro-scale solutions, in the metamodeling approach, was developed for larger dimensionality and subsequent calibration. An analysis of the present metamodeling approach indicates improved performance in comparison to previous studies.

scholarly journals Effective Models for Long Time Wave Propagation in Locally Periodic Media

2018 ◽  
Vol 56 (5) ◽  
pp. 2701-2730 ◽  
Author(s):  
Assyr Abdulle ◽  
Timothée Pouchon
Keyword(s):  
Wave Propagation ◽  
Periodic Media ◽  
Long Time ◽  
Effective Models
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