skip to main content

Title: Multilevel Monte Carlo for two phase flow and Buckley–Leverett transport in random heterogeneous porous media

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
Resource Relation:
Journal Name: Journal of Computational Physics; 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)
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