New question #156163 on DOLFIN: https://answers.launchpad.net/dolfin/+question/156163
Hi all, I'm attempting to implement a depth averaged ice-sheet flow model in dolfin. I'm starting with something called the shallow-shelf approximation, which is, in essence, a depth averaged version of Stokes' flow (with a non-linear viscosity). I very much like the interface of FEniCs because of the dimensionally independent problem definition notation, and I would like to define my model using the VectorFunctionSpace construct. My problem is that in the depth averaged equations, I end up needing a tensor like this : [ 2ux + vy , uy+vx ] [ uy + vx , 2vy+ux ] where u and v are velocities (the solution) and ux, uy, vx, and vy are their spatial derivatives. This tensor can be broken into two parts: [ 2ux , uy+vx ] + [vy, 0 ] [ uy + vx , 2vy] [ 0, ux] The first component is just the 2D strain rate tensor that you get with sym(grad(u)), if u is a trial function over a VectorFunctionSpace. My question is how to achieve the second part, or more generally, how can I construct the necessary tensor (the first one that I wrote), while maintaining VectorFunctionSpace type notation? Presumably, I could write the model using two separate scalar variables u and v, and invoking the spatial derivative and as_tensor operator a whole bunch of times ... but that's not nearly as pleasant, so I would be grateful for any assistance. Also, if anyone has any demos of depth-averaged fluid flow (e.g. shallow water equations) that you wouldn't mind sharing, I would appreciate taking a look. Preferably in Python. Cheers. -- You received this question notification because you are a member of DOLFIN Team, which is an answer contact for DOLFIN. _______________________________________________ Mailing list: https://launchpad.net/~dolfin Post to : dolfin@lists.launchpad.net Unsubscribe : https://launchpad.net/~dolfin More help : https://help.launchpad.net/ListHelp
