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arXiv · 2507.03192

Parallel multilevel methods for solving the Darcy--Forchheimer model based on a nearly semicoercive formulation

Jongho Park·S. Majid Hassanizadeh
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Abstract

High-velocity fluid flow through porous media is modeled by prescribing a nonlinear relationship between the flow rate and the pressure gradient, called the Darcy--Forchheimer equation. This paper is concerned with the analysis of parallel multilevel methods for solving the Darcy--Forchheimer model. We begin by reformulating the Darcy--Forchheimer model as a nearly semicoercive convex optimization problem via the augmented Lagrangian method. Building on this formulation, we develop a parallel multilevel method, also known as a multilevel additive Schwarz method, within the framework of subspace correction for nearly semicoercive convex problems, yielding a theoretically supported and computationally efficient solver for the Darcy--Forchheimer model. The convergence analysis establishes robustness with respect to the augmented Lagrangian parameter $\epsilon$. To further enhance convergence, we incorporate a backtracking line search and a full approximation scheme. Numerical results support the theoretical findings and demonstrate the effectiveness of the proposed approach.

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Jongho Park, S. Majid Hassanizadeh. 2025-07-03. Parallel multilevel methods for solving the Darcy--Forchheimer model based on a nearly semicoercive formulation. https://arxiv.org/abs/2507.03192

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