On Wed, Dec 12, 2012 at 10:52 AM, Allawala, Altan <[email protected]>wrote:
> Hi Daniel, > > It can be seen that there is an internal boundary condition implicit in > the equation which is that psi(x=0,y=0) is constant in time. This will be only obeyed with a cell center directly at y=0. Otherwise that condition has no impact on the final solution at any place away from 0. Each layer is independent as there is no lateral communication. > And so the initial Gaussian function sets this to be 1 throughout the > evolution. Yet this boundary condition is not maintained. Isn't that > strange? > It will be maintained for cells directly at y=0. In the example I wrote up, none of the cells are positioned directly at y=0. > > Also, is there no way that FiPy can solve this problem over the full > domain then? > There probably is a trick to do this, but I can't think of it right now. I am a little confused as to how to deal with the quadrants in which the source term is the "wrong" sign. Am I right in saying that the steady state solution in each quadrant is symmetric with the other quadrants? The other question is whether the steady state solution you're trying to find is stable. One thing is that if you look at the equation in the top left quadrant the solution seems to be unbounded. Taking the initial solution, $\psi_x$ seems to be positive always, y is positive and the source is always negative so it would seem that it can just keep growing unless $\psi_x$ flips sign (this may indicate that a different scheme is needed to calculate the $\psi_x$ that somehow stabilises the solution if the solution is stable). A careful stability analysis may be helpful here before doing the numerical solution. I'm not even really sure if this is a good candidate problem for a FV solver. > > Thanks for the input. > No problem. Hope it works out. -- Daniel Wheeler
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