Multilevel Monte Carlo for two phase flow and Buckley–Leverett transport in random heterogeneous porous media
Abstract
Monte Carlo (MC) is a well known method for quantifying uncertainty arising for example in subsurface flow problems. Although robust and easy to implement, MC suffers from slow convergence. Extending MC by means of multigrid techniques yields the multilevel Monte Carlo (MLMC) method. MLMC has proven to greatly accelerate MC for several applications including stochastic ordinary differential equations in finance, elliptic stochastic partial differential equations and also hyperbolic problems. In this study, MLMC is combined with a streamline-based solver to assess uncertain two phase flow and Buckley–Leverett transport in random heterogeneous porous media. The performance of MLMC is compared to MC for a two dimensional reservoir with a multi-point Gaussian logarithmic permeability field. The influence of the variance and the correlation length of the logarithmic permeability on the MLMC performance is studied.
- Authors:
- Publication Date:
- OSTI Identifier:
- 22230802
- Resource Type:
- Journal Article
- Journal Name:
- Journal of Computational Physics
- Additional Journal Information:
- Journal Volume: 250; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; CONVERGENCE; CORRELATIONS; MONTE CARLO METHOD; PARTIAL DIFFERENTIAL EQUATIONS; PERFORMANCE; PERMEABILITY; POROUS MATERIALS; RANDOMNESS; STOCHASTIC PROCESSES; TWO-DIMENSIONAL CALCULATIONS; TWO-PHASE FLOW
Citation Formats
Müller, Florian, Jenny, Patrick, and Meyer, Daniel W., E-mail: meyerda@ethz.ch. Multilevel Monte Carlo for two phase flow and Buckley–Leverett transport in random heterogeneous porous media. United States: N. p., 2013.
Web. doi:10.1016/J.JCP.2013.03.023.
Müller, Florian, Jenny, Patrick, & Meyer, Daniel W., E-mail: meyerda@ethz.ch. Multilevel Monte Carlo for two phase flow and Buckley–Leverett transport in random heterogeneous porous media. United States. https://doi.org/10.1016/J.JCP.2013.03.023
Müller, Florian, Jenny, Patrick, and Meyer, Daniel W., E-mail: meyerda@ethz.ch. 2013.
"Multilevel Monte Carlo for two phase flow and Buckley–Leverett transport in random heterogeneous porous media". United States. https://doi.org/10.1016/J.JCP.2013.03.023.
@article{osti_22230802,
title = {Multilevel Monte Carlo for two phase flow and Buckley–Leverett transport in random heterogeneous porous media},
author = {Müller, Florian and Jenny, Patrick and Meyer, Daniel W., E-mail: meyerda@ethz.ch},
abstractNote = {Monte Carlo (MC) is a well known method for quantifying uncertainty arising for example in subsurface flow problems. Although robust and easy to implement, MC suffers from slow convergence. Extending MC by means of multigrid techniques yields the multilevel Monte Carlo (MLMC) method. MLMC has proven to greatly accelerate MC for several applications including stochastic ordinary differential equations in finance, elliptic stochastic partial differential equations and also hyperbolic problems. In this study, MLMC is combined with a streamline-based solver to assess uncertain two phase flow and Buckley–Leverett transport in random heterogeneous porous media. The performance of MLMC is compared to MC for a two dimensional reservoir with a multi-point Gaussian logarithmic permeability field. The influence of the variance and the correlation length of the logarithmic permeability on the MLMC performance is studied.},
doi = {10.1016/J.JCP.2013.03.023},
url = {https://www.osti.gov/biblio/22230802},
journal = {Journal of Computational Physics},
issn = {0021-9991},
number = ,
volume = 250,
place = {United States},
year = {Tue Oct 01 00:00:00 EDT 2013},
month = {Tue Oct 01 00:00:00 EDT 2013}
}