On Thu, Oct 15, 2009 at 12:10 PM, Borden, Doug <[email protected]> wrote: > > Daniel, the solutions tend not to be dissipative. They are convective > between regions, where the > region boundaries are determined both exogenously (the different “tj’s”) and > endogenously, by > the value of psi = eta phi + eta x + dphi/dx passing the threshholds +/- > epsilon. At the region > boundaries, neither dphi/dx nor dphi/dt exists, but phi is continuous across > the region boundaries. > I suspect what I really need is a grid that knows to adjust to have edges at > the boundary regions, > and only requires continuity of phi but not dphi at those locations.
I don't believe that you should have to do anything special to the grid. In my experience, this is the wrong way to think about the problem. It should be a variable that maps the boundary region and is artificially smooth and the variable is included in your equations in some way via coefficients. Although, fipy might not be ideal for this problem, it might be worth trying out the VanLeerConvectionTerm as the convective operator. It is second order accurate (apart from when it is flux limiting) and has flux limiting, which may be useful if this problem has sharp changes in the variables being solved for. In the end you may need a higher order term still, but this could at least form a basis to improve on. -- Daniel Wheeler
