A duality method for the compressible Reynolds equation. Application to simulation of read/write processes in magnetic storage devices

In this work the authors present a new numerical algorithm to approximate the solution of compressible Reynolds equation with additional first-order slip flow terms. This equation appears when modelling read/write processes in magnetic storage devices such as hard disks. The proposed numerical method is based on characteristics approximation for convection (dominating) terms and a duality method applied to a maximal monotone operator which represents the nonlinear diffusive term. Several test examples illustrate the good performance of the method.