On Mar 14, 2013, at 9:33 PM, Edwin Sze Lun Khoo wrote:
> I am having difficulties with trying to put a PDE into a form that FiPy
> accepts. The equation in question is dC/dt + alpha*d/dx(1/C) = d^2C/dx^2
> where C is the dependent variable and alpha is a constant. The first and last
> terms are just the standard TransientTerm and DiffusionTerm respectively, but
> the second term is a ConvectionTerm with a variable that is the reciprocal of
> the dependent variable. FiPy doesn't accept the keyword var=1/C when defining
> an equation, while casting d/dx(1/C) as a source term causes the solver to
> stop converging when there are sharp gradients are in C. What are some other
> ways of recasting this PDE? Thanks!
You can try running the chain rule on it:
\alpha\frac{\partial}{\partial x}\frac{1}{C}
= -\frac{\alpha}{C^2}\frac{\partial C}{\partial x}
so you get a "normal" convection term with a velocity of -alpha/C**2.
Otherwise, you'll need to declare that term explicitly.
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