Journal ArticleDOI
The transition between the Stokes equations and the Reynolds equation: a mathematical proof
Guy Bayada,Michèle Chambat +1 more
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In this paper, it was shown that the Reynolds equation is an approximation of the Stokes equation and that the kind of convergence is strongly related with the boundary conditions on the velocity field.Abstract:
The Reynolds equation is used to calculate the pressure distribution in a thin layer of lubricant film between two surfaces. Using the asymptotic expansion in the Stokes equations, we show the existence of singular perturbation phenomena whenever the two surfaces are in relative motion. We prove that the Reynolds equation is an approximation of the Stokes equations and that the kind of convergence is strongly related with the boundary conditions on the velocity field.read more
Citations
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The Impact of the Cavitation Model in the Analysis of Microtextured Lubricated Journal Bearings
TL;DR: In this article, the impact of the cavitation model on the numerical assessment of lubricated journal bearings is analyzed and compared using the classical Reynolds model and the so-called p- θ model proposed by Elrod and Adams.
Journal ArticleDOI
The polynomial property of self-adjoint elliptic boundary-value problems and an algebraic description of their attributes
TL;DR: In this article, a wide class of boundary-value problems for which the application of elliptic theory can be reduced to elementary algebraic operations is described and characterized by the following polynomial property: the sesquilinear form corresponding to the problem degenerates only on some finite-dimensional linear space of vector polynomials.
Journal ArticleDOI
Полиномиальное свойство самосопряженных эллиптических краевых задач и алгебраическое описание их атрибутов@@@The polynomial property of self-adjoint elliptic boundary-value problems and an algebraic description of their attributes
Journal ArticleDOI
Moving textures: Simulation of a ring sliding on a textured liner
Hugo M Checo,Roberto F. Ausas,Mohammed Jai,Jean Paul Cadalen,Franck Choukroun,Gustavo C. Buscaglia +5 more
TL;DR: In this article, numerical simulations of the ring/liner contact in which the liner exhibits a periodic texture (pockets) are reported, and the authors show that the ring profile determines whether pocketing is beneficial or not.
References
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Book
Navier-Stokes Equations
TL;DR: Schiff's base dichloroacetamides having the formula OR2 PARALLEL HCCl2-C-N ANGLE R1 in which R1 is selected from the group consisting of alkenyl, alkyl, alkynyl and alkoxyalkyl; and R2 is selected by selecting R2 from the groups consisting of lower alkylimino, cyclohexenyl-1 and lower alkynyl substituted cycloenenyl -1 as discussed by the authors.
Journal ArticleDOI
On the Theory of Lubrication and Its Application to Mr. Beauchamp Tower's Experiments, Including an Experimental Determination of the Viscosity of Olive Oil
TL;DR: In this paper, the authors considered the boundary or surface actions of fluids and proposed a theoretical treatment of the physical actions of oils and other viscous fluids to diminish friction and wear between solid surfaces.
BookDOI
Finite element approximation of the Navier-Stokes equations
TL;DR: A mixed finite element method for solving the stokes problem and the time-dependent navier-stokes equations are presented.