Such flows are involved in numerous physical and engineering problems from automobile fuel injectors to fusion reactor design. I would like to learn about efficient implementation of schemes in two or three space dimensions, discovering how best to organize the computation for a variety of different machine architectures, chiefly clustered SMP machines. When simulating gas dynamics on a vector machine with an implicitly defined equation of state, it is common to iterate only a fixed number of times, rather than to convergence, per computational zone to solve the equation of state.
Similar tradeoffs ought to exist for more complicated models.
I believe that I can make a contribution by adding to the understanding of how to make careful compromises in the underlying physics and chemistry, and in the formal statement of the scheme, that leave the scheme effective while speeding computation.