On numerical solution of nonlinear parabolic multicomponent diffusion-reaction problems

Abstract

This work continues our previous analysis concerning the numerical solution of the multi-component mass transfer equations. The present test problems are two-dimensional, parabolic, non-linear, diffusion- reaction 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. The numerical results obtained show good numerical performances.

Splitting Algorithm for Numerical Solving of Parabolic Nonlinear Multi - Component Convection – Diffusion Mass Transfer Equations

“…To verify the splitting error, the present test problem was also solved numerically using the fully implicit method from [30,31] combined with the defect -correction iteration [32] (in order to achieve second-order accuracy). The values of the relative differences between the present results (average concentrations) and those provided by the fully implicit method are smaller than 1%.…”