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.
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Acknowledgements
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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Arregui, I., Cendán, J.J., González, M. (2019). Application of a Local Discontinuous Galerkin Method to the 1D Compressible Reynolds Equation. In: García Guirao, J., Murillo Hernández, J., Periago Esparza, F. (eds) Recent Advances in Differential Equations and Applications. SEMA SIMAI Springer Series, vol 18. Springer, Cham. https://doi.org/10.1007/978-3-030-00341-8_4
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