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A duality method for the compressible Reynolds equation. application to simulation of read/write processes in magnetic storage devices. (English) Zbl 1107.76030

Summary: 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.

MSC:

76D08 Lubrication theory
34B15 Nonlinear boundary value problems for ordinary differential equations
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76N99 Compressible fluids and gas dynamics
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