Application of a Local Discontinuous Galerkin Method to the 1D Compressible Reynolds Equation

Abstract

In this work we present a numerical method to approximate the solution of the steady-state compressible Reynolds equation with additional first-order slip flow terms. This equation models the hydrodynamic features of read/write processes in magnetic storage devices such as hard disks. The numerical scheme is based on the local discontinuous Galerkin method proposed by Cockburn and Shu (SIAM J Numer Anal 35:2440–2463, 1998), which shows good properties in the presence of internal layers appearing in convection-diffusion problems. Several test examples illustrate the good performance of the method.