Pressure statistics from the path integral for Darcy flow through random porous media
| Autor: | Marise J. E. Westbroek, Peter King, Dimitri D. Vvedensky, Gil-Arnaud Coche |
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| Rok vydání: | 2019 |
| Předmět: |
DYNAMICS
Statistics and Probability Discretization Physics Multidisciplinary MODELS FOS: Physical sciences General Physics and Astronomy 01 natural sciences Darcy–Weisbach equation 010305 fluids & plasmas Physics - Geophysics pressure symbols.namesake Stochastic differential equation porous media 0103 physical sciences Statistics Neumann boundary condition 010306 general physics 01 Mathematical Sciences Mathematical Physics Mathematics Science & Technology 02 Physical Sciences Darcy's law Physics Fluid Dynamics (physics.flu-dyn) Statistical and Nonlinear Physics Markov chain Monte Carlo random permeability Physics - Fluid Dynamics Computational Physics (physics.comp-ph) Geophysics (physics.geo-ph) Physics Mathematical Permeability (earth sciences) Markov chain Monte Carlo method Modeling and Simulation Physical Sciences SIMULATION Path integral formulation Darcy equation symbols Physics - Computational Physics path integral |
| Zdroj: | Journal of Physics A: Mathematical and Theoretical. 52:185001 |
| ISSN: | 1751-8121 1751-8113 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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