GENERIC formalism and discrete variational derivative method for the two-dimensional vorticity equation

The vorticity equation for two-dimensional incompressible viscous flows is formulated within the GENERIC formalism for non-equilibrium thermodynamics. The laws of conservation of energy and increasing entropy derived from the GENERIC formulation are properly inherited by the finite difference equati...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2016-04, Vol.296, p.690-708
Main Authors: Suzuki, Yukihito, Ohnawa, Masashi
Format: Article
Language:English
Subjects:
Derivatives
Discrete variational derivative method
Entropy
Formalism
GENERIC formulation
Incompressible flow
Mathematical analysis
Mathematical models
Two dimensional
Vorticity equations
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Summary:The vorticity equation for two-dimensional incompressible viscous flows is formulated within the GENERIC formalism for non-equilibrium thermodynamics. The laws of conservation of energy and increasing entropy derived from the GENERIC formulation are properly inherited by the finite difference equations obtained by invoking the discrete variational derivative method. The law of increasing entropy corresponds to the dissipation of enstrophy for the vorticity equation. Some numerical experiments have been done to examine the usefulness of the proposed method.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2015.10.018