Hi everyone,
I’m trying to solve a rather simple expression:
where alpha, kappa and viscosity are constants. The domain is over a cylinder. I know the pressure within the inner lumen and at the outer lumen. I’ve expressed the weak form of the equation (1) as:
F = u*v*dx + ((poro*permeability)/viscosity)*v*grad(p)*dx
My questions are:

How do I express my boundary conditions? Since I only know the pressure and not the velocity

Currently, I’ve worked out an expression for Pressure assuming a linear distribution as follows:
pressure = Expression("((P_lumen  P_adv)/vessel_thickness)*pow((pow(x[0],2) + pow(x[1],2)),0.5)", degree=1, P_lumen=p_inner_lumen,
P_adv=p_adventitia, vessel_thickness=vessel_thickness)
p = interpolate(pressure,V)However, I’m not sure if I’m supposed to assume this or treat it as another variable to be solved?

How do I implement the 2nd equation? I’ve been trying to follow this but since my form does not have a temporal domain I find it rather confusing.