flux/darcyslaw.hh File Reference

Advective fluxes according to Darcy's law. More...

#include <dumux/flux/darcyslaw_fwd.hh>
#include <dumux/flux/cctpfa/darcyslaw.hh>
#include <dumux/flux/ccmpfa/darcyslaw.hh>
#include <dumux/flux/cvfe/darcyslaw.hh>

Go to the source code of this file.

Description

Advective fluxes according to Darcy's law.

Darcy's law describes the advective flux in porous media on the macro-scale and is valid in the creeping flow regime (Reynolds number << 1, Forchheimer extensions is also implemented->see forcheimerslaw.hh). The advective flux characterizes the bulk flow for each fluid phase including all components in case of compositional flow. It is driven by the potential gradient $\textbf{grad}\, p - \varrho {\textbf g}$, accounting for both pressure-driven and gravitationally-driven flow. The velocity is proportional to the potential gradient with the proportional factor $\frac{\textbf K}{\mu}$, including the intrinsic permeability of the porous medium, and the viscosity µ of the fluid phase. For one-phase flow it is:

$$v = - \frac{\mathbf K}{\mu} \left(\textbf{grad}\, p - \varrho {\mathbf g} \right)$$

This equation can be extended to calculate the velocity $v_\alpha$ of phase $\alpha$ in the case of multi-phase flow by introducing a relative permeability $k_{r\alpha}$ restricting flow in the presence of other phases:

$$v_\alpha = - \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K} \left(\text{grad}\, p_\alpha - \varrho_{\alpha} \mathbf{g} \right)$$

Darcy's law is specialized for different discretization schemes. This file contains the data which is required to calculate volume and mass fluxes of fluid phases over a face of a finite volume by means of the Darcy approximation. See the corresponding header files for the specific different discretization methods.

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