A robust iterative scheme for the slightly compressible Darcy-Forchheimer equations

TL;DR

This paper introduces a new iterative linearization scheme for solving the nonlinear algebraic systems arising from discretizing the slightly compressible Darcy-Forchheimer equations, with demonstrated robustness and efficiency.

Contribution

The paper develops and analyzes a general iterative linearization method tailored for the nonlinear systems from Darcy-Forchheimer equations, improving solution robustness and efficiency.

Findings

The proposed scheme converges reliably at the discrete level.

Numerical experiments show the scheme's robustness with discontinuous permeability fields.

The method outperforms standard iterative solvers in nonlinear regimes.

Abstract

We study the slightly compressible Darcy-Forchheimer equations modeling gas flow in porous media, particularly in applications related to combustion processes. The equations are discretized in time using the backward Euler method and in space via a mixed finite element scheme. As a result, a nonlinear algebraic system is obtained at each time step. We propose and analyze a general iterative linearization scheme for the efficient solution of such systems and study its convergence properties at the discrete level. The performance and robustness of the scheme are assessed through a series of numerical experiments. The method is compared with standard iterative solvers, and further tested on problems with discontinuous permeability fields. The results demonstrate its reliability and competitiveness in regimes characterized by strong nonlinear effects.