Evaluation of the path integral for flow through random porous media.
basic_science · Level V
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- Record sourced from PubMed, PMID 29758682.
- Also identified by DOI 10.1103/PhysRevE.97.042119.
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Abstract
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 dimensions is discussed.