Multi-Solver and Multi-Grid Sampling for Fast, Non-Intrusive, and Versatile Uncertainty Quantification of Two-Phase Flow and Transport

Abstract:

Multilevel Monte Carlo (MLMC) combines traditionally a multigrid technique with Monte Carlo (MC) sampling (see figure) to arrive at a MC simulation framework that is substantially faster than conventional MC. Here, we apply instead of grids of different resolution a hierarchy of solution methods of different accuracy. In the context of two-phase flow and transport, we demonstrate that the resulting solver MLMC leads like traditional MLMC to significant speedups while offering greater flexibility in certain applications. We document the performance gain of MLMC over MC for different exemplary quantities like mean water saturation distributions and oil production curves, but also relevant scalar quantities.