Journal
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
Volume 26, Issue 13, Pages 2393-2449Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202516500573
Keywords
Ferrofluids; incompressible flows; microstructure; micropolar flows; magnetic fluid flow; angular momentum; magnetization
Categories
Funding
- NSF Grant [DMS-1109325, DMS-1411808, DMS-1418784]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1411808] Funding Source: National Science Foundation
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We discuss the equations describing the motion of ferrofluids subject to an external magnetic field. We concentrate on the model proposed by Rosensweig, provide an appropriate definition for the effective magnetizing field, and explain the simplifications behind this definition. We show that this system is formally energy stable, and devise a numerical scheme that mimics the same stability estimate. We prove that solutions of the numerical scheme always exist and, under further simplifying assumptions, that the discrete solutions converge. We also discuss alternative formulations proposed in pre-existing work, primarily involving a regularization of the magnetization equation and supply boundary conditions which lead to an energy stable system. We present a series of numerical experiments which illustrate the potential of the scheme in the context of real applications.
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