A joint position-velocity Fokker-Planck framework for advective-diffusive transport is introduced, with closure-based velocity-PDF equations whose stationary solutions match the Eulerian velocity distribution in Poiseuille flow.
Probability density function of non- reactive solute concentration in heterogeneous porous formations.Journal of contaminant hydrology, 94(1-2):109–125, 2007
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Probability density function (PDF) models for particle transport in porous media
A joint position-velocity Fokker-Planck framework for advective-diffusive transport is introduced, with closure-based velocity-PDF equations whose stationary solutions match the Eulerian velocity distribution in Poiseuille flow.