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The pressure and flow statistics of Darcy flow through a random permeablemedium are expressed in a form suitable for evaluation by the method ofsimulated annealing. There are several attractive aspects to using simulatedannealing: (i) any probability distribution can be used for the permeability,(ii) there is no need to invert the transmissibility matrix which, while not afactor for single-phase flow, offers distinct advantages for the case ofmultiphase flow, and (iii) the action used for simulated annealing is eminentlysuitable for coarse graining by integrating over the short-wavelength degreesof freedom. In this paper, we show that the pressure and flow statisticsobtained by simulated annealing are in excellent agreement with the moreconventional finite-volume calculations.

Pressure and flow statistics of Darcy flow from simulated annealing