# Mathematical analysis and numerical simulation of a Reynolds-Koiter model for the elastohydrodynamic journal-bearing device

Iñigo Arregui; J. Jesús Cendán; Carlos Vázquez

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 36, Issue: 2, page 325-343
- ISSN: 0764-583X

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topArregui, Iñigo, Jesús Cendán, J., and Vázquez, Carlos. "Mathematical analysis and numerical simulation of a Reynolds-Koiter model for the elastohydrodynamic journal-bearing device." ESAIM: Mathematical Modelling and Numerical Analysis 36.2 (2010): 325-343. <http://eudml.org/doc/194107>.

@article{Arregui2010,

abstract = {
The aim of this work is to deduce the existence of solution
of a coupled problem arising in elastohydrodynamic
lubrication. The lubricant pressure and concentration are
modelled by Reynolds equation, jointly with the free-boundary
Elrod-Adams model in order to take into account cavitation
phenomena. The bearing deformation is solution of Koiter
model for thin shells. The existence of solution to the
variational problem presents some difficulties: the coupled
character of the equations, the nonlinear multivalued
operator associated to cavitation and the fact of writing the
elastic and hydrodynamic equations on two different domains.
In a first step, we regularize the Heaviside operator.
Additional difficulty related to the different
domains is circumvented by means of prolongation and
restriction operators, arriving to a regularized coupled
problem. This one is decoupled into elastic and hydrodynamic
parts, and we prove the existence of a fixed point for the
global operator. Estimations obtained for the
regularized problem allow us to prove the existence of
solution to the original one. Finally, a numerical method is proposed in order
to simulate a real journal-bearing device and illustrate the qualitative and
quantitative properties of the solution.
},

author = {Arregui, Iñigo, Jesús Cendán, J., Vázquez, Carlos},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Koiter model; Reynolds equation; free boundary problems; fixed point techniques.; fixed point techniques; fixed point},

language = {eng},

month = {3},

number = {2},

pages = {325-343},

publisher = {EDP Sciences},

title = {Mathematical analysis and numerical simulation of a Reynolds-Koiter model for the elastohydrodynamic journal-bearing device},

url = {http://eudml.org/doc/194107},

volume = {36},

year = {2010},

}

TY - JOUR

AU - Arregui, Iñigo

AU - Jesús Cendán, J.

AU - Vázquez, Carlos

TI - Mathematical analysis and numerical simulation of a Reynolds-Koiter model for the elastohydrodynamic journal-bearing device

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 36

IS - 2

SP - 325

EP - 343

AB -
The aim of this work is to deduce the existence of solution
of a coupled problem arising in elastohydrodynamic
lubrication. The lubricant pressure and concentration are
modelled by Reynolds equation, jointly with the free-boundary
Elrod-Adams model in order to take into account cavitation
phenomena. The bearing deformation is solution of Koiter
model for thin shells. The existence of solution to the
variational problem presents some difficulties: the coupled
character of the equations, the nonlinear multivalued
operator associated to cavitation and the fact of writing the
elastic and hydrodynamic equations on two different domains.
In a first step, we regularize the Heaviside operator.
Additional difficulty related to the different
domains is circumvented by means of prolongation and
restriction operators, arriving to a regularized coupled
problem. This one is decoupled into elastic and hydrodynamic
parts, and we prove the existence of a fixed point for the
global operator. Estimations obtained for the
regularized problem allow us to prove the existence of
solution to the original one. Finally, a numerical method is proposed in order
to simulate a real journal-bearing device and illustrate the qualitative and
quantitative properties of the solution.

LA - eng

KW - Koiter model; Reynolds equation; free boundary problems; fixed point techniques.; fixed point techniques; fixed point

UR - http://eudml.org/doc/194107

ER -

## References

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