[CFDN00b]

I'm not very knowledgeable in CFD but I made a fluid solver along the lines of
http://http.developer.nvidia.com/GPUGems3/gpugems3_ch30.html
which I believe is an LBM representation using partial MacCormack methods for a solver (my method has no jacobi solver or any others for that matter and streams velocities and particles,etc. and then applies a simple diffusion equation to the results). I have problems with implementing the implicit Euler in "Melting and Flowing" by Mark Carlson, Peter J. Mucha, R. Brooks Van Horn III and Greg Turk. because of the matrices which I do not use (use vectors and scalars instead) I think I could figure out what the Laplacian operator is but I don't see how I could implement it in my framework. Anyone who understands how to add the high viscosities without adding an integrator/matrices or doing non-vector/non-algebra math would be most welcome.
On a second note: is what I'm looking for even possible? Does anyone know of any source code for a melting and solidifying LBM solver that I can study?