# How do I simulate a constant velocity flow in porous media

I am modelling gas combustion in porous media. Most contemporary models assume that the pressure drop from the porous media is small enough to disregard, but I want to include that in my investigation. Most studies alos assume that the gas is filtered through the media at a constant speed $u$.

I use Darcy's law to couple the velocity and pressure feilds:

$u=-\frac{k}{\mu}\nabla p$.

Plus we have the ideal gas euqation of state and the continuity equation:

$p=\rho RT/M_r$

$\frac{\partial \rho}{\partial t}+\nabla \cdot (\rho u)=0$.

Since we are talking about combustion the case is not isothermal, two energy euqations are also present. All the quations are solved with finite differences.

I first of all want to qualitatively reproduce the results obtained in previous studies to validate my model. The question is how do I simulate a constant velocity in the domain. It seems like the Darcy equation implues that I should apply a proper pressure drop, i.e first order boundary conditions on the pressure. This implies a big pressure drop if I want to obtain something around $u=0.5$ m/s in the camera. Moreover the velocity appears to be increasing rapidly towards the far end, where atmosperic pressure is prescribed.

I was thinking perhaps that I ran into this problem limitation as a payment for not solving a real Navier-Stockes. But I am not sure, so here I am :).

P.S. I do realize that I can through away the gasodynamical part of the model and just prescribe the speed in the energy equations as far as validation goes, I have indeed done that and got good results.