# Pressure and flow statistics of Darcy flow from simulated annealing

## TL;DR

This paper demonstrates that simulated annealing can effectively compute pressure and flow statistics in Darcy flow through random media, matching traditional methods and offering advantages for complex permeability distributions.

## Contribution

It introduces a novel application of simulated annealing for Darcy flow statistics, highlighting its flexibility and computational benefits over conventional methods.

## Key findings

- Simulated annealing results agree with finite-volume calculations.
- The method handles arbitrary permeability distributions.
- Advantages include no matrix inversion and suitability for multiphase flow.

## Abstract

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