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

被引：44

作者：

Mueller, Florian ^{[1
]}

Jenny, Patrick ^{[1
]}

Meyer, Daniel W. ^{[1
]}

机构：

[1] ETH, Inst Fluid Dynam, CH-8092 Zurich, Switzerland

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2013年 / 250卷

关键词：

Multilevel Monte Carlo; Random heterogeneous porous media; Two phase flow; Two phase transport; Streamline solver; FINITE-VOLUME METHODS; PROBABILISTIC COLLOCATION; CONSERVATION-LAWS;

D O I：

10.1016/j.jcp.2013.03.023

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

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. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：685 / 702

页数：18

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