"Simpler" algorithm, parallel processing
 

I'm working on a cfd code to simulate a bubble plume (2-d), in water with 2-way coupling.
I'm interested in parallelizing the code. (As of now, it's completely serial). Can anyone suggest ways to parallelize the Eulerian part (Simpler algorithm is used. Line wise TDMA to solve 2-d linear equations). Is there an algorithm to parallelize the line wise TDMA?
Thanks in advance

parallel TDMA can be found in the book
"Parallel Scientific Computing in C++ and MPI"