SIAM Journal on Scientific Computing
Multilevel Monte Carlo Methods
LSSC '01 Proceedings of the Third International Conference on Large-Scale Scientific Computing-Revised Papers
Multilevel Monte Carlo Path Simulation
Operations Research
Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients
Computing and Visualization in Science
Journal of Computational Physics
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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.