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Algebraic multigrid methods for uncertainty quantification of source-type flows through randomly heterogeneous porous media.

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Title: Algebraic multigrid methods for uncertainty quantification of source-type flows through randomly heterogeneous porous media.
Authors: Schiano Di Cola, Vincenzo1 (AUTHOR), Cuomo, Salvatore2 (AUTHOR), Severino, Gerardo3 (AUTHOR), Berardi, Marco1 (AUTHOR) marco_berardi@rocketmail.com
Source: Applied Numerical Mathematics. Dec2025, Vol. 218, p58-72. 15p.
Subjects: Algebraic multigrid methods, Finite volume method, Monte Carlo method, Porous materials, Random fields
Abstract: We consider steady flow generated by a source through a porous medium where, due to its erratic variations in the space, the conductivity K is regarded as a random field. As a consequence, flow variables become stochastic, and we aim at quantifying their uncertainty. To this purpose, we use Monte Carlo simulations, where for each realization the governing flow equation is solved by a finite volume method. This yields a deterministic linear system solved by algebraic multigrid (AMG) techniques. By leveraging analytical solutions valid for homogeneous (constant K) formations, we first compare different AMG solvers, that are subsequently used as trial in order to extend our approach to heterogeneous porous media. Results demonstrate that AMG methods enable achieving, especially at higher iteration counts, an L 2 -error lower than other, Gaussian-type, approximations. • Groundwater equation, accounting for the spatial variability of the conductivity, is solved within a stochastic framework. • AMG solver is used for facing groundwater flow driven by Dirac-type sink/source. • AMG methods achieve efficient solutions adopting a finite volume framework. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:We consider steady flow generated by a source through a porous medium where, due to its erratic variations in the space, the conductivity K is regarded as a random field. As a consequence, flow variables become stochastic, and we aim at quantifying their uncertainty. To this purpose, we use Monte Carlo simulations, where for each realization the governing flow equation is solved by a finite volume method. This yields a deterministic linear system solved by algebraic multigrid (AMG) techniques. By leveraging analytical solutions valid for homogeneous (constant K) formations, we first compare different AMG solvers, that are subsequently used as trial in order to extend our approach to heterogeneous porous media. Results demonstrate that AMG methods enable achieving, especially at higher iteration counts, an L 2 -error lower than other, Gaussian-type, approximations. • Groundwater equation, accounting for the spatial variability of the conductivity, is solved within a stochastic framework. • AMG solver is used for facing groundwater flow driven by Dirac-type sink/source. • AMG methods achieve efficient solutions adopting a finite volume framework. [ABSTRACT FROM AUTHOR]
ISSN:01689274
DOI:10.1016/j.apnum.2025.06.015