Hello Fipy,
I've run into a problem in designing/implementing my model and was wondering what the best practice would be. Currently, I am trying to model a 1D PDE that is a cell species, H, along a linear axis, x: \begin{equation}\label{FiPyFinal} \underbrace{\frac{\delta H}{\delta t}}_{Transient} + \underbrace{(v_A + C_\Phi \Phi \frac{\delta S}{\delta x})\frac{\delta H}{\delta x}}_{Convection} = \underbrace{D\frac{\delta^2 H}{\delta x^2}}_{Diffusion} + \underbrace{r_H C_A A H\Big(1 - \frac{\bar{H}}{K_H}\Big) - \delta_H H - \delta_D S H}_{Source} \end{equation} H is the cell species I am interested in modeling, but S and A are also CellVariables. Currently they are invariant, but this will probably change as the model develops. Importantly, \bar{H} is the total population of H. \Phi is also a globally calculated feedback function. My questions pertain to uncertainty in how to implement the Convection and Source terms. For the source term: I see in the FiPy docs that for source terms, "The dependence can only be included in a linear manner". So does this imply that the correct way to implement this source term would be: ImplicitSourceTerm(coeff = r_H * C_A * A * (1 - H_bar()/K_H) - delta_H - delta_D * S) With H_bar() being a function: # Set up the summing of HSCs def H_bar(): return H.cellVolumeAverage * mesh.cellVolumes.sum() Am I incorrect in manually computing H_bar() at every timestep and then using it as the source term coefficient? Also, will there be any problems with A and S also being CellVariables in this coupled PDE system? For the Convection term: And as another question, for the convection term, is it appropriate to have it as: ConvectionTerm(coeff = v_A + C_phi + Phi() + S.faceGrad) As in the source term, will there be issues with having Phi() as a function which changes at every timestep? Thank you, Derek Park --------------------------- Derek Park | D. Phil student, University of Oxford
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