Solver-based vs. grid-based multilevel Monte Carlo for two phase flow and transport in random heterogeneous porous media

We consider two phase flow and transport in heterogeneous porous media with uncertain permeability distribution. The resulting transport uncertainty is assessed by means of multilevel Monte Carlo (MLMC). In contrast to the Monte Carlo (MC) method, which operates on one specific numerical grid with one numerical solver, MLMC samples from a hierarchy of grids or numerical solvers. In this work, the MLMC performance resulting from a hierarchy consisting of a finite volume transport solver and a streamline-based solver is compared to a purely grid-based hierarchy. Unlike the established grid-based MLMC method, our solver-based MLMC method operates on the same numerical grid and therefore avoids difficulties related to the upscaling of permeability fields or boundary conditions on coarser grids. For a two dimensional test case with log-normal permeability distribution, both MLMC approaches are compared to a MC reference run. At equivalent accuracy, significant speedups of MLMC with respect to MC are achieved.