Uncertainty quantification in coastal aquifers using the multilevel Monte Carlo method

AbstractWe are solving a problem of salinisation of coastal aquifers. As a test case example, we consider the Henry saltwater intrusion problem. Since porosity, permeability and recharge are unknown or only known at a few points, we model them using random fields and random variables. The Henry problem describes a two‐phase flow and is non‐linear and time‐dependent. The solution to be found is the expectation of the salt mass fraction, which is uncertain and time‐dependent. To estimate this expectation, we use the well‐known multilevel Monte Carlo (MLMC) method. The MLMC method takes just a few samples on computationally expensive (fine) meshes and more samples on cheap (coarse) meshes. Then, by building a telescoping sum, the MLMC method estimates the expected value at a much lower computational cost than the classical Monte Carlo method. The deterministic solver used here is the well‐known parallel and scalable ug4 solver.