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Comparing Darcy’s Law and the Brinkman Equation for Numerical Simulations of Saltwater Intrusion

Author

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  • Jingwei Yao

    (School of Engineering and Built Environment, Griffith University, Gold Coast, QLD 4222, Australia)

  • Hong Zhang

    (School of Engineering and Built Environment, Griffith University, Gold Coast, QLD 4222, Australia)

Abstract

Saltwater intrusion into coastal aquifers presents a significant global challenge to fresh groundwater resources. Numerical modelling represents a valuable tool to study this phenomenon. Darcy’s Law is widely applied to groundwater studies and is extended into the Brinkman Equation to account for kinetic dissipations due to viscous shear. However, their comparative performance and accuracy in density-driven flows remain unclear. To determine the circumstances where the Brinkman Equation is required, numerical simulations with both models were implemented in hypothetical coastal aquifer scenarios. The results revealed that the largest discrepancies between the two models occur inside the dispersion zone during the break-through period, with concentration differences of up to 2.5%. The mixing of freshwater and saltwater induces rapid density and velocity variations. Brinkman’s viscous term moderates the rate of change and decreases the intrusion length by up to 6.1 m in a 180 m intrusion case. Furthermore, higher permeability and a lower recharge rate both strengthen the viscous effects in most sandy coastal aquifers. The Brinkman Equation excels at capturing intricate flow patterns with large variations. Therefore, it is necessary to be employed for studies on freshwater–saltwater interfaces and other similar conditions including groundwater–surface water interfaces, non-isothermal flows, and complex geological conditions.

Suggested Citation

  • Jingwei Yao & Hong Zhang, 2023. "Comparing Darcy’s Law and the Brinkman Equation for Numerical Simulations of Saltwater Intrusion," Sustainability, MDPI, vol. 15(18), pages 1-16, September.
    • Handle: RePEc:gam:jsusta:v:15:y:2023:i:18:p:13287-:d:1233207
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    References listed on IDEAS

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    1. Pažanin, Igor & Radulović, Marko, 2020. "Effects of the viscous dissipation on the Darcy-Brinkman flow: Rigorous derivation of the higher-order asymptotic model," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    2. Gongbo Long & Yingjie Liu & Wanrong Xu & Peng Zhou & Jiaqi Zhou & Guanshui Xu & Boqi Xiao, 2022. "Analysis of Crack Problems in Multilayered Elastic Medium by a Consecutive Stiffness Method," Mathematics, MDPI, vol. 10(23), pages 1-16, November.
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