Jacobian-Free Newton-Krylov with a globalization method for solving groundwater flow models of multi-layer aquifer systems

TL;DR

This paper introduces a Jacobian-Free Newton-Krylov (JFNK) method with a globalization scheme to efficiently solve large nonlinear systems in groundwater flow models of multi-layer aquifers, validated against traditional methods.

Contribution

The paper presents a novel JFNK method with globalization for groundwater models, demonstrating improved efficiency and adaptability over existing Newton-Krylov approaches.

Findings

JFNK outperforms NK in computational efficiency for complex models.

Validation shows JFNK results align with NK method.

JFNK effectively integrated into existing hydrologic models.

Abstract

A Jacobian free Newton Krylov (JFNK) method with a globalization scheme is introduced to solve large and complex nonlinear systems of equations that arise in groundwater flow models of multi-layer aquifer systems. We explore the advantages of the JFNK method relative to the Newton-Krylov (NK) method and identify the circumstances in which the JFNK method demonstrates computing efficiency. We perform the validation and efficiency of the JFNK method on various test cases involving an unconfined single-layer aquifer and a two-layer aquifer with both confined and unconfined conditions. The results are validated by the NK method. The JFNK method is incorporated in Integrated Water Flow Model (IWFM), an integrated hydrologic model developed and maintained by California Department of Water Resources. We examine the determinacy of the JFNK's adaptability on practical models such as the California Central Valley Groundwater-Surface Water Simulation Model (C2VSim).