We consider a class of density-driven flow problems. We are particularly
interested in the problem of the salinization of coastal aquifers. We consider
the Henry saltwater intrusion problem with uncertain porosity, permeability,
and recharge parameters as a test case. The reason for the presence of
uncertainties is the lack of knowledge, inaccurate measurements, and inability
to measure parameters at each spatial or time location. This problem is
nonlinear and time-dependent. The solution is the salt mass fraction, which is
uncertain and changes in time. Uncertainties in porosity, permeability,
recharge, and mass fraction are modeled using random fields. This work
investigates the applicability of the well-known multilevel Monte Carlo (MLMC)
method for such problems. The MLMC method can reduce the total computational
and storage costs. Moreover, the MLMC method runs multiple scenarios on
different spatial and time meshes and then estimates the mean value of the mass
fraction. The parallelization is performed in both the physical space and
stochastic space. To solve every deterministic scenario, we run the parallel
multigrid solver ug4 in a black-box fashion. We use the solution obtained from
the quasi-Monte Carlo method as a reference solution.Comment: 24 pages, 3 tables, 11 figure