Application of a Local Discontinuous Galerkin Method to the 1D Compressible Reynolds Equation
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.
KeywordsCompressible flows Reynolds equation Local discontinuous Galerkin method
This research was partially supported by the Spanish Government (Ministerio de Economía y Competitividad) under projects MTM2013-47800-C2-1-P and MTM2016-76497-R.
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