| 1. |
- Almqvist, Andreas, et al.
(författare)
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Homogenization of the unstationary incompressible Reynolds equation
- 2007
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Ingår i: Tribology International. - : Elsevier BV. - 0301-679X .- 1879-2464. ; 40:9, s. 1344-1350
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Tidskriftsartikel (refereegranskat)abstract
- This paper is devoted to the effects of surface roughness during hydrodynamic lubrication. In the numerical analysis a very fine mesh is needed to resolve the surface roughness, suggesting some type of averaging. A rigorous way to do this is to use the general theory of homogenization. In most works about the influence of surface roughness, it is assumed that only the stationary surface is rough. This means that the governing Reynolds type equation does not involve time. However, recently, homogenization was successfully applied to analyze a situation where both surfaces are rough and the lubricant is assumed to have constant bulk modulus. In this paper we will consider a case where both surfaces are assumed to be rough, but the lubricant is incompressible. It is also clearly demonstrated, in this case that homogenization is an efficient approach. Moreover, several numerical results are presented and compared with those corresponding to where a constant bulk modulus is assumed to govern the lubricant compressibility. In particular, the result shows a significant difference in the asymptotic behavior between the incompressible case and that with constant bulk modulus.
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| 2. |
- Almqvist, Andreas, et al.
(författare)
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A new approach for studying cavitation in lubrication
- 2014
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Ingår i: Journal of tribology. - : ASME International. - 0742-4787 .- 1528-8897. ; 136:1
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Tidskriftsartikel (refereegranskat)abstract
- The underlying theory, in this paper, is based on clear physical arguments related to conservation of mass flow and considers both incompressible and compressible fluids. The result of the mathematical modeling is a system of equations with two unknowns, which are related to the hydrodynamic pressure and the degree of saturation of the fluid. Discretization of the system leads to a linear complementarity problem (LCP), which easily can be solved numerically with readily available standard methods and an implementation of a model problem in matlab code is made available for the reader of the paper. The model and the associated numerical solution method have significant advantages over today's most frequently used cavitation algorithms, which are based on Elrod-Adams pioneering work
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| 3. |
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| 4. |
- Almqvist, Andreas, et al.
(författare)
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Flow in thin domains with a microstructure : Lubrication and thin porous media
- 2017
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Ingår i: AIP Conference Proceedings. - : AIP Publishing. - 0094-243X .- 1551-7616. ; 1798
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Tidskriftsartikel (refereegranskat)abstract
- This paper is devoted to homogenization of different models of flow in thin domains with a microstructure. The focus is on applications connected to the effect of surface roughness in full film lubrication, but a parallel to flow in thin porous media is also discussed. Mathematical models of such flows naturally include two small parameters. One is connected to the fluid film thickness and the other to the microstructure. The corresponding asymptotic analysis is a delicate problem, since the result depends on how fast the two small parameters tend to zero relative to each other. We give a review of the current status in this area and point out some future challenges.
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| 7. |
- Almqvist, Andreas, et al.
(författare)
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Homogenization of a Reynolds equation describing compressible flow
- 2012
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Ingår i: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X .- 1096-0813. ; 390:2, s. 456-471
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Tidskriftsartikel (refereegranskat)abstract
- We homogenize a Reynolds equation with rapidly oscillating film thickness function hε, assuming a constant compressiblity factor in the pressure-density relation. The oscillations are due to roughness on the bounding surfaces of the fluid film. As shown by previous studies, homogenization is an effective approach for analyzing the effects of surface roughness in hydrodynamic lubrication. By two-scale convergence theory we obtain the limit problem (homogenized equation) and strong convergence in L2 for the unknown density ρε. By adding a small corrector term we also obtain strong convergence in the Sobolev norm.
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| 9. |
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| 10. |
- Almqvist, Andreas, et al.
(författare)
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Homogenization of the Reynolds equation
- 2013
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Ingår i: Encyclopedia of Tribology. - Berlin : Springer-Verlag New York Inc.. - 9780387928968 - 9780387928975 ; , s. 1685-1690
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Bokkapitel (refereegranskat)
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