Solver-based vs. grid-based multilevel Monte Carlo for two phase flow and 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 equations in finance, elliptic stochastic partial differential equations and also hyperbolic problems. In this study, MLMC is combined with a streamlinebased solver to assess uncertain two phase flow and transport in random heterogeneous porous media. The performance of MLMC is compared to MC for a two dimensional reservoir with multi-point Gaussian logarithmic permeability fields. The influence of the variance and the correlation length of the logarithmic permeability on the MLMC performance is studied.