Convection describes the movement of a species, such as a pollutant, with the bulk fluid velocity. The velocity field u corresponds to a superficial volume average over a unit volume of the porous medium, including both pores and matrix. This velocity is sometimes called
Darcy velocity, and defined as volume flow rates per unit cross section of the medium. This definition makes the velocity field continuous across the boundaries between porous regions and regions with free flow.
The average linear fluid velocities ua, provides an estimate of the fluid velocity within the pores:
where εp is the porosity and
θ =
sεp the liquid volume fraction, and
s the saturation, a dimensionless number between 0 and 1.
When using the non-conservative formulation, which is the default, the fluid is assumed incompressible and divergence free: ∇ ⋅ u =
0. The non-conservative formulation improves the stability of systems coupled to a momentum equation (fluid flow equation).