Evaluation of the path integral for flow through random porous media.

  title={Evaluation of the path integral for flow through random porous media.},
  author={Marise J. E. Westbroek and Gil-Arnaud Coche and Peter R. King and Dimitri D. Vvedensky},
  journal={Physical review. E},
  volume={97 4-1},
We present a path integral formulation of Darcy's equation in one dimension with random permeability described by a correlated multivariate lognormal distribution. This path integral is evaluated with the Markov chain Monte Carlo method to obtain pressure distributions, which are shown to agree with the solutions of the corresponding stochastic differential equation for Dirichlet and Neumann boundary conditions. The extension of our approach to flow through random media in two and three… 

Figures from this paper

Pressure statistics from the path integral for Darcy flow through random porous media

The path integral for classical statistical dynamics is used to determine the properties of one-dimensional Darcy flow through a porous medium with a correlated stochastic permeability for several

Pressure and flow statistics of Darcy flow from simulated annealing

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 and are in excellent agreement with the more conventional finite-volume calculations.

Path integral Monte Carlo method for the quantum anharmonic oscillator

The Markov chain Monte Carlo (MCMC) method is used to evaluate the imaginary-time path integral of a quantum oscillator with a potential that includes a quadratic term and a quartic term whose

Stochastic Lagrangians for noisy dynamics



Calculation of the effective permeability of a randomly inhomogeneous porous medium

The effective permeability of a porous medium is calculated nonperturbatively. An exact expression for the permeability in terms of a double path integral is derived on the assumption that the

Path-integral methods for turbulent diffusion

We derive a path-integral representation for the effective diffusion function of a passive scalar field. We use it to calculate the long-time effective diffusivity in Gaussian turbulence in the

Hydrodynamic Screening in Random Media

We study the propagation of momentum through viscous fluid in a domain containing a large number of randomly distributed small obstacles. The obstacles are assumed to be fixed, and the velocity is

Inertial Effects on Fluid Flow through Disordered Porous Media

We investigate the origin of the deviations from the classical Darcy law by numerical simulation of the Navier-Stokes equations in two-dimensional disordered porous media. We apply the Forchheimer

The use of field theoretic methods for the study of flow in a heterogeneous porous medium

The effects of heterogeneities on the steady state flow of a single fluid in a porous medium are examined. It is argued that incomplete knowledge of the permeability requires the use of a stochastic

Flow in porous media I: A theoretical derivation of Darcy's law

Stokes flow through a rigid porous medium is analyzed in terms of the method of volume averaging. The traditional averaging procedure leads to an equation of motion and a continuity equation


We present an overview of the lattice Boltzmann method (LBM), a parallel and efficient algorithm for simulating single-phase and multiphase fluid flows and for incorporating additional physical

Cellular‐automaton fluids: A model for flow in porous media

Numerical models of fluid flow through porous media can be developed from either microscopic or macroscopic properties. The large‐scale viewpoint is perhaps the most prevalent. Darcy’s law relates

Stochastic Modeling of the Permeability of Randomly Generated Porous Media via the Lattice Boltzmann Method and Probabilistic Collocation Method

The permeability of natural porous media, such as soils and rocks, usually possesses uncertainties due to the randomness and spatial variation of microscopic pore structures. It is of great

Functional integral approach to classical statistical dynamics

The functional integral method for the statistical solution of stochastic differential equations is extended to a broad, new class of nonlinear dynamical equations with random coefficients and