Optimization of a finite volume differencing scheme for multispecies transport problem

I am working on a 3d finite volume scheme for an advection-diffusion- reaction problem involving a large number of chemical species (more than 60) and a large domain (an big lake for example). Since this scheme will be used on large problem, I want it to be as efficient as possible. The linear operators are splitted in 2 :

(1) advection-diffusion is solved using a fully implicit finite volume discretisation with a multigrid method for solving the linear system of equations (2) chemistry is solved using a Runge-Kutta-Rosenbrock solver for stiff ODE.

The transport (1) actually have the following form

foreach specie in speciesList { construct_matrix(); solve_linear_system();

}

and takes a lot of time on the computer.

Assuming that diffusion coefficients are the same for all species, the whole fluid (including all species) should follow the same path during the transport. I wonder if it really necessairy to loop over all species and compute the transport several time. It is possible to compute the transport of the fluid once, and after reuse this calculation to the different species ?

I would really appreciate suggestion or reference on this.

Maybe I could do the following :

1) Suppose I use a fully implicit (backward Euler for example) or semi- implicit (Crank-nicholson) time integrating scheme. I will use a finite volume discretisation to create a linear system in the form

A * c(n+1) =3D c(n)

2) Compute

T =3D inverse(A)

Using a finite volume discretisation, with an hybrid differencing scheme (central/upwind depending on the Peclet number) for the advective part, the matrix A will be diagonnally dominant and all entries are positive. Hence, the inverse of A exists and could be computer with an appropriate method (any suggestions on an efficient way to do this ?)

3) loop over all species and solve

C(n+1) =3D T * C(n)

for each one.