Hello to the FiPy Team: I was recently reviewing some old work and thinking of converting it over to FiPy and realized that, while I had done some successful work in FiPy (with your assistance several times), there are a few gaps in my knowledge of how to apply FiPy to some CFD type problems. I apologize for asking questions you may feel are clear in your guide, but I am trying to learn how to use your awesome program a bit better so I don't have to keep asking questions.
I'm essentially looking at coupling the continuity equation for a fluid
with the equations for motion or the equations of change. So, we start with
this:
\nabla(\rho*v) = -\frac{\partial \rho}{\partial t}
But frequently I have a steady state situation in which:
\nabla(\rho*v) = 0
In either case, I'm not sure how the continuity equation up in FiPy. Do you
have any suggestions? Should I set up multiple convection terms like this:
PowerLawConvectionTerm(coeff=rho, var = v_x) +
PowerLawConvectionTerm(coeff=rho, var = v_y) +
PowerLawConvectionTerm(coeff=rho, var = v_z) = 0
Similarly, we have momentum equations as:
\nabla(\rho v_x) = -\frac{\partial{P}}{\partial x} +\rho g_x + \mu
\nabla^2v_x
\nabla(\rho v_y) = -\frac{\partial{P}}{\partial y} +\rho g_y + \mu
\nabla^2v_y
\nabla(\rho v_z) = -\frac{\partial{P}}{\partial z} +\rho g_z + \mu
\nabla^2v_z
I frequently am able to ignore the \rho g_i term but if I didn't, I believe
I could treat this as a source term in Fipy, and simply add it to my
equation. I understand how to do the diffusion and convection terms, from
your guides.
However, I don't know what to do with the pressure term. I don't usually
have a consistent pressure in all dimensions so I would think that the
pressure term should be a cell variable, but I don't know how to add it. I
tried treating it as P.faceGrad, but I get errors. I've tried it as a
PowerLawConvectionTerm, and I don't seem to get a result. Perhaps the
problem is with the continuity equation?
As a sort of classic example, I've uploaded a code that describes two
plates with a fluid in between. In it, fluid is flowing between two plates.
The bottom plate is stationary, the top one is moving. There's a pressure
difference over the length of the plates. It's at steady state, but I'll
probably end up playing with it as a non-steady state system eventually.
I've tried it before, and perhaps I'm graphing it incorrectly, but it seems
like it just presents a steady state solution.
If I've got this completely wrong, could you suggest how to set up a
continuity equation coupled with a momentum equation and, perhaps how to
handle a first order differential term like the pressure gradient?
Thank you,
--
Daniel DeSantis
Two-plate flow example.py
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