TY - JOUR
T1 - GENERIC formalism and discrete variational derivative method for the two-dimensional vorticity equation
AU - Suzuki, Yukihito
AU - Ohnawa, Masashi
PY - 2016/4/1
Y1 - 2016/4/1
N2 - 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.
AB - 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.
KW - Discrete variational derivative method
KW - GENERIC formulation
KW - Vorticity equations
UR - http://www.scopus.com/inward/record.url?scp=84946893582&partnerID=8YFLogxK
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U2 - 10.1016/j.cam.2015.10.018
DO - 10.1016/j.cam.2015.10.018
M3 - Article
AN - SCOPUS:84946893582
VL - 296
SP - 690
EP - 708
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
SN - 0377-0427
ER -