InTheHole
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Don't believe me? I don't blame you, I don't know that I would if I were in your position. Try this on for size:
I'm doing my thesis proposal defense in the last week of August. The main focus of my research is tissue growth in a porous seeded scaffold in a perfusion bioreactor. The system we're analyzing is a coupled system of two equations, one defining the culture medium in the domain (steady-state), and the other describing the change in cell density (time-dependent). A group in Nottingham analyzed a model like this in a two-phase paper, in which they use the Navier-Stokes equations to build their model. Ours doesn't quite work in the same manner as we didn't start with the N-S equations, we just used standard conservation of mass principles. As such, we can use Darcy's Law to get an averaged fluid velocity in the domain, and then we don't have to explicitly calculate the shear stress in the pores. We've got a complete model in 1-D, on which will be the basis of my proposal, and right now I'm working on expanding it into two dimensions. I've gotten as far as solving -div(k grad p)=0 with k (the permeability) varying and thus the problem is not quite a standard Laplace equation. We can still use an Ax=b solver used for Laplace's equation to solve this, such as conjugate gradient or gmres. Next, I need to solve the equation for the culture medium in two dimensions using a 2-D interpolation like bilinear or bicubic interpolation for the x and y direction fluid velocity. How does that suit you?
