The p-Laplacian: phenomenological modelling of the flow in porous media and CFD simulations
Petr Girg, Luk\'a\v{s} Kotrla, and Ane\v{z}ka \v{S}vandov\'a
TL;DR
This paper explores the use of the p-Laplacian in modeling groundwater flow in porous media, analyzing mathematical properties and employing CFD simulations to estimate parameters in fractured aquifers.
Contribution
It connects the p-Laplacian to hydrological models, examines maximum principles, and applies CFD to realistic fracture network scenarios for parameter estimation.
Findings
Conditions for maximum principles in p-Laplacian models
Validation of models with CFD simulations
Parameter estimation for fractured aquifers
Abstract
The aim of this paper is to discuss several aspects of connections between the p-Laplacian and mathematical models in hydrology. At first we present models of groundwater flow in phreatic aquifers and models of irrigation and drainage that lead to quasilinear parabolic equations involving the p-Laplacian. Next, we survey conditions of validity of Strong Maximum Principle and Strong Comparison Principle for this type of problems. Finally, we employ computer fluid dynamics simulations to realistic scenario of fracture networks to estimate values of the parameters of constitutive laws governing groundwater flow in the context of fractured hard-rock aquifers.
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