Analysis of Heterogeneous Multiscale Methods for Long Time Wave Propagation Problems

2014 ◽  
Vol 12 (3) ◽  
pp. 1135-1166 ◽  
Author(s):  
Doghonay Arjmand ◽  
Olof Runborg
Keyword(s):  
Wave Propagation ◽  
Multiscale Methods ◽  
Long Time ◽  
Heterogeneous Multiscale

scholarly journals FE heterogeneous multiscale method for long-time wave propagation

2013 ◽  
Vol 351 (11-12) ◽  
pp. 495-499 ◽  
Author(s):  
Assyr Abdulle ◽  
Marcus J. Grote ◽  
Christian Stohrer
Keyword(s):  
Wave Propagation ◽  
Multiscale Method ◽  
Long Time ◽  
Heterogeneous Multiscale

A Brief Review of Previous Studies on Regularity of Stress Waves Propagation in Micro-Cracks of Rock

2012 ◽  
Vol 170-173 ◽  
pp. 511-515
Author(s):  
Jin Yu ◽  
Yan Yan Cai ◽  
Bo Xue Song ◽  
Xu Chen
Keyword(s):  
Wave Propagation ◽  
Stress Wave ◽  
Mathematic Model ◽  
Practical Significance ◽  
Theoretical Interpretation ◽  
Stress Wave Propagation ◽  
Micro Cracks ◽  
Propagation Law ◽  
Mechanism Research ◽  
Long Time

The research of stress wave propagation law under cracked rock has important theoretical value and practical significance. Because of the discontinuity, nonelasticity and nonlinearity of the cracks, the theoretical interpretation and mechanism research about tress wave propagation law are a great challenge to researchers for a long time. From the establishment of the research method, the determination of mathematic model of micro-cracks and the main solutions, this paper brief reviews the current development of the influence of the complicated micro-cracks on stress wave propagation law.

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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