What is it about?

We investigated the applicability and efficiency of the MLMC approach to the Henry-like problem with uncertain porosity, permeability and recharge. These uncertain parameters were modelled by random fields with three independent random variables. Permeability is a function of porosity. Both functions are time-dependent, have multi-scale behaviour and are defined for two layers. The numerical solution for each random realisation was obtained using the well-known ug4 parallel multigrid solver.

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Why is it important?

Although the deterministic Henry problem is well-known, the difficulties here are that it is not clear how input uncertainties propagate through the non-linear, time-dependent problem. The solution to be found is then the mean value and the variance of the salt mass fraction, both are functions of space and time. From an implementation point of view, we test how easy it is to couple multigrid and multilevel Monte Carlo solvers.


An accurate estimate of the output uncertainties can facilitate a better understanding of the Henry saltwater problem, better decisions, and improved control and design of the experiment.

Dr. Alexander Litvinenko
Rheinisch Westfalische Technische Hochschule Aachen

Read the Original

This page is a summary of: Uncertainty quantification in the Henry problem using the multilevel Monte Carlo method, Journal of Computational Physics, February 2024, Elsevier,
DOI: 10.1016/j.jcp.2024.112854.
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