smolarkiewicz's deformational flow
 

hi. I am trying to simulate smolarkiewicz's deformational flow (P.K. Smolarkiewicz, The multi-dimensional Crowley advection scheme, Mon. Wea. Rev. 110 (1982) 1968-1983)

And I am trying to find the exact solution. the exact solution of the problem is given in the "A. Staniforth, J. Côté, J. Pudykiewicz, Comments on "Smolarkiewicz's deformational flow", Mon. Wea. Rev. 115 (1987) 894-900"
Jacobian Elliptic function is needed to find the exact solution. I tried to write a program to get the exact solution. but it doest work.

could you tell me where I can find the exact solution or a program that computes?
I will really appreciate any contribution.

Thanks in advance

Did you try finding the exact solution symbolically using either mathematica/maxima. If it is not feasible, did you try looking for Blas libraries for fortran/c++ or using matlab/octave.