Adaptive numerical methods for an hydrodynamic problem arising in magnetic reading devices

The mechanical behavior of magnetic reading devices is mainly governed by compressible Reynolds equations when the air bearing modeling approximation is considered. First, the convection dominated feature motivates the use of a characteristics scheme adapted to steady state problems. Secondly, a duality method to treat the particular nonlinear diffusion term is applied. A piecewise linear finite element for spatial discretization has been chosen. Moreover, in certain conditions and devices, strong air pressure gradients arise locally, either due to a strongly convection dominated regime or to the presence of slots in the storage device, for example. In the present work we improve the previous numerical methods proposed to cope with this new setting. Thus, mainly adaptive mesh refinement algorithms based on pressure gradient indicators and appropriate multigrid techniques to solve the linear systems arising at each iteration of the duality method are proposed. Finally, several examples illustrate the performance of the set of numerical techniques.