The Darcy problem with porosity depending exponentially on the pressure

TL;DR

This paper analyzes a model of viscous fluid flow through porous media where permeability depends exponentially on pressure, including a splitting formulation, discretization, and error analysis.

Contribution

It introduces a novel exponential pressure-dependent permeability model and provides a comprehensive analysis and discretization approach with error estimates.

Findings

Permeability depends exponentially on pressure.

A splitting formulation effectively models the flow.

Error bounds are established for the discretization.

Abstract

We consider the flow of a viscous incompressible fluid through a porous medium. We allow the permeability of the medium to depend exponentially on the pressure and provide an analysis for this model. We study a splitting formulation where a convection diffusion problem is used to define the permeability, which is then used in a linear Darcy equation. We also study a discretization of this problem, and provide an error analysis for it.