Jens Eberhard 2004 J. Phys. A: Math. Gen. 37 9587 doi:10.1088/0305-4470/37/40/018
Jens Eberhard
Show affiliationsThis paper focuses on upscaling of the transport equation for heterogeneous porous media with random flow. We consider the local flow field being a stationary random field and develop an upscaling by the recently developed coarse graining method which is based on filtering procedures in Fourier space. The coarse graining method is used to obtain an upscaled dispersion tensor which depends on the given length scale of the upscaling. We give explicit results for the scale-dependent dispersion coefficient in lowest-order perturbation theory. For finite length scales the upscaled dispersion models the effect of the unresolved subscale flow fluctuations, and for a global upscaling the upscaled value agrees with the well-known macrodispersion coefficient, which is, however, nearly approached for length scales larger than tenfold of the correlation length.
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
76S05 Flows in porous media; filtration; seepage
82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)
Issue 40 (8 October 2004)
Received 11 June 2004, in final form 17 August 2004
Published 22 September 2004
Jens Eberhard 2004 J. Phys. A: Math. Gen. 37 9587
Norman Dombey and Fuad M Saradzhev 2000 J. Phys. A: Math. Gen. 33 4491
Giovanni Montani et al 2003 Class. Quantum Grav. 20 4195
Tilman Enss et al 2004 J. Phys. A: Math. Gen. 37 10479
D. J. Christian et al. 2008 ApJ 686 542
P Schlottmann and A A Zvyagin 2002 J. Phys. A: Math. Gen. 35 6191
Tomasz Dietl 2002 Semicond. Sci. Technol. 17 377
Moh'd Rezeq et al 2009 Supercond. Sci. Technol. 22 125018
Jan L Cieśliński and Waldemar Biernacki 2005 J. Phys. A: Math. Gen. 38 9491
Elena R Loubenets 2001 J. Phys. A: Math. Gen. 34 7639