Imperial College London
Professor John Gibbon

ProfessorJohnGibbon

Faculty of Natural Sciences, Department of Mathematics

Senior Research Investigator
 
 
 
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Contact

 

j.d.gibbon Website

 
 
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Location

 

6M41Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Gibbon:2016:10.1103/PhysRevE.94.063103,
author = {Gibbon, JD and Pal, N and Gupta, A and Pandit, R},
doi = {10.1103/PhysRevE.94.063103},
journal = {Physical Review E},
title = {Regularity criterion for solutions of the three-dimensional Cahn-Hilliard-Navier-Stokes equations and associated computations},
url = {http://dx.doi.org/10.1103/PhysRevE.94.063103},
volume = {94},
year = {2016}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We consider the three-dimensional (3D) Cahn-Hilliard equations coupled to, and driven by, the forced, incompressible 3D Navier-Stokes equations. The combination, known as the Cahn-Hilliard-Navier-Stokes (CHNS) equations, is used in statistical mechanics to model the motion of a binary fluid. The potential development of singularities (blow-up) in the contours of the order parameter  is an open problem. To address this we have proved a theorem that closely mimics the Beale-Kato-Majda theorem for the 3D incompressible Euler equations [J. T. Beale, T. Kato, and A. J. Majda, Commun. Math. Phys. 94, 61 (1984)]. By taking an L∞ norm of the energy of the full binary system, designated as E∞, we have shown that ∫t0E∞(τ)dτ governs the regularity of solutions of the full 3D system. Our direct numerical simulations (DNSs) of the 3D CHNS equations for (a) a gravity-driven Rayleigh Taylor instability and (b) a constant-energy-injection forcing, with 1283 to 5123 collocation points and over the duration of our DNSs confirm that E∞ remains bounded as far as our computations allow.
AU  - Gibbon,JD
AU  - Pal,N
AU  - Gupta,A
AU  - Pandit,R
DO  - 10.1103/PhysRevE.94.063103
PY  - 2016///
SN  - 2470-0045
TI  - Regularity criterion for solutions of the three-dimensional Cahn-Hilliard-Navier-Stokes equations and associated computations
T2  - Physical Review E
UR  - http://dx.doi.org/10.1103/PhysRevE.94.063103
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000397422700011&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - http://hdl.handle.net/10044/1/57657
VL  - 94
ER  -
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