This paper deals with the implementation on the Grid'5000 network, the French grid platform, of parallel simulations for the solution of a 3D coupled boundary value problem. This problem models continuous flow electrophoresis which is governed by Navier Stokes equations coupled with convection-diffusion and potential equations. The coupled boundary value problems are discretised by appropriate schemes involving the convergence of the parallel synchronous and asynchronous Schwarz alternating algorithms. Finally, parallel experiments on grid computing are presented and analyzed.