Numerical solution of a 1-D elastohydrodynamic problem in magnetic storage devices
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 42 (2008) no. 4, p. 645-665

In this work we present new numerical methods to simulate the mechanics of head-tape magnetic storage devices. The elastohydrodynamic problem is formulated in terms of a coupled system which is governed by a nonlinear compressible Reynolds equation for the air pressure over the head, and a rod model for the tape displacement. A fixed point algorithm between the solutions of the elastic and hydrodynamic problems is proposed. For the nonlinear Reynolds equation, a characteristics method and a duality algorithm are developed to cope with the convection dominating and nonlinear diffusion features, respectively. Furthermore, in the duality method the convergence and optimal choice of the parameters are analyzed. At each fixed point iteration, in the elastic model a complementarity formulation is required and appropriate numerical techniques are used. For the spatial discretization different finite element spaces are chosen. Finally, numerical test examples illustrate the theoretical results, as well as the good performance in the simulation of real devices.

Classification:  76A20,  76D08,  35J60,  65J15,  65N60
Keywords: head-tape devices, elastohydrodynamic lubrication, compressible Reynolds equation, rod model, duality methods, finite elements
     author = {Arregui, I\~nigo and Cend\'an, Jos\'e Jes\'us and Par\'es, Carlos and V\'azquez, Carlos},
     title = {Numerical solution of a 1-D elastohydrodynamic problem in magnetic storage devices},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {42},
     number = {4},
     year = {2008},
     pages = {645-665},
     doi = {10.1051/m2an:2008021},
     zbl = {pre05318504},
     mrnumber = {2437777},
     language = {en},
     url = {}
Arregui, Iñigo; Cendán, José Jesús; Parés, Carlos; Vázquez, Carlos. Numerical solution of a 1-D elastohydrodynamic problem in magnetic storage devices. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 42 (2008) no. 4, pp. 645-665. doi : 10.1051/m2an:2008021.

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