On numerical solution of nonlinear parabolic multicomponent convection-diffusion problems

In this work, we analyze the numerical solving of the multi-component mass transfer equations. The present test problems are two-dimensional, parabolic, non-linear, convection-diffusion equations. An implicit finite difference method was used to discretize the mathematical model equations. The algorithm used to solve the non-linear system resulted for each time step is the modified Picard iteration. The numerical performances of the preconditioned conjugate gradient algorithms (BICGSTAB and GMRES) in solving the linear systems of the modified Picard iteration were analysed in detail. For all the combinations of the parameters, we obtained a stable solution. The values of the convergence rate obtained show that the present numerical solution is second-order accurate in space. The values of the convergence rate and efficiency of the preconditioned GMRES and BiCGSTAB algorithms are similar those usually reported in literature for non-linear convection diffusion problems. (author)