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Investigating the Adaptability of ALE-AMR Hydrocode for Darcy Flow and Geothermal Simulations

Authors:
Alice Koniges
David Eder
Jonghyun Lee
Jiawei Shen
Aaron Fisher
Tzanio Kolev

Keywords: ALE-AMR; Darcy flow; geothermal simulation; porous media; finite element method; MFEM; hydrocode; computational fluid dynamics.

Abstract:
The PISALE ALE-AMR hydrocode suite is an advanced computational tool that combines the Arbitrary Lagrangian-Eulerian (ALE) method with Adaptive Mesh Refinement (AMR) to simulate complex multi-physics problems involving substantial material deformation. The suite currently includes physics modules for heat conduction and radiation transport, which are handled by a finite element diffusion solver operating on a structured, adaptive mesh infrastructure provided by the SAMRAI library. This paper investigates the feasibility of extending this framework to simulate fluid flow in porous media as described by Darcy's law, a critical component for subsurface applications like geothermal energy extraction and hydrogeology. We analyze the mathematical parallels between diffusion and Darcy flow, assess the suitability of the existing solver, and consider the integration of the more general MFEM finite element library. The primary objective is to evaluate the potential of the ALE-AMR methodology for Darcy flow simulations and to outline the necessary modifications and implementation steps, including addressing challenges related to integrating different AMR and grid formulations.

Pages: 8 to 14

Copyright: Copyright (c) IARIA, 2025

Publication date: September 28, 2025

Published in: conference

ISSN: 2308-4499

ISBN: 978-1-68558-289-0

Location: Lisbon, Portugal

Dates: from September 28, 2025 to October 2, 2025