Uncertainty quantification in coastal aquifers using the multilevel Monte Carlo method

Alexander Litvinenko, Dmitry Logashenko, Raul Tempone, Ekaterina Vasilyeva, Gabriel Wittum

Research output: Contribution to journalArticlepeer-review


We 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.
Original languageEnglish (US)
StatePublished - Sep 15 2023

Bibliographical note

KAUST Repository Item: Exported on 2023-09-18
Acknowledgements: The authors thank the KAUST HPC support team for their assistance with Shaheen II. This work was supported by the Alexander von Humboldt Foundation. Open access funding enabled and organized by Projekt DEAL.


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