TY - JOUR

T1 - Uncertainty quantification in coastal aquifers using the multilevel Monte Carlo method

AU - Litvinenko, Alexander

AU - Logashenko, Dmitry

AU - Tempone, Raul

AU - Vasilyeva, Ekaterina

AU - Wittum, Gabriel

N1 - 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.

PY - 2023/9/15

Y1 - 2023/9/15

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/690154

UR - https://onlinelibrary.wiley.com/doi/10.1002/pamm.202300005

U2 - 10.1002/pamm.202300005

DO - 10.1002/pamm.202300005

M3 - Article

SN - 1617-7061

JO - PAMM

JF - PAMM

ER -