[sahm]

Hi everyone,

I am trying to make a boundary condition for my solver that keeps the mass flow rate constant (I need to mention that it's solving diffusion of gas in porous medium). I cannot assume k and gradient of P as constant or uniform as they change over the boundary condition.
The method I'm trying to do for this boundary condition is to assume a small volume before the boundary condition, and set a pressure that changes over time (similar to what happens in the experiment). The pressure variation is calculated as:

dP/dt * (V/RT) = m ̇_(bc )−m ̇_r

V is the volume of the boundary condition space (it's tubing in my experiment), R is gas constant, T is temperature of the gas, is the desired flow rate defined in the boundary condition, is the flow rate at the boundary that is calculated as:

m ̇= ∫ −k/μ ∇P.(P/RT) dA

Now the problem is that gets bigger than and that will reduce the boundary condition pressure. This causes the simulation to blow up if P becomes negative. I have to make dt very small for this to work, or I have to define this boundary condition as implicit. Can you guys tell me how to make it implicit? Something like:

(P^(n+1)−P^n) / Δt = RT/V (m ̇_(bc) − m ̇_r^ (n+1) )

If you have any suggestion for any other method to define this boundary condition, I would like to hear it.