2018/11/05 by Marise J. E. Westbroek, Gil-Arnaud Coche, Peter R. King +1
Computer Science · Environmental Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Discretization #Gaussian #Geology #Geotechnical engineering #Groundwater flow and contamination studies #Mathematical analysis #Mathematics #Path integral formulation #Physics #Porosity #Porous medium #Statistical physics #Theoretical and Computational Physics #physics.comp-ph #physics.flu-dyn #physics.geo-ph
paper · pdf · doi:10.1088/1751-8121/ab1100
arxiv created 2018/11/05 · openalex publication_date 2019/03/19 · arxiv updated 2019/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract 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 spatial correlation lengths. Pressure statistics are obtained from the numerical evaluation of the path integral by using the Markov chain Monte Carlo method. Comparisons between these pressure distributions and those calculated from the classic finite-volume method for the corresponding stochastic differential equation show excellent agreement for Dirichlet and Neumann boundary conditions. The evaluation of the variance of the pressure based on a continuum description of the medium provides an estimate of the effects of discretization. Log-normal and Gaussian fits to the pressure distributions as a function of position within the porous medium are discussed in relation to the spatial extent of the correlations of the permeability fluctuations.