A Numerical technique for solving carrier-mediated transport problems

Abstract

A numerical technique and a computer program based on the method of orthogonal collocation on finite elements for solving steady state carrier-mediated transport problems is presented. The method is especially suitable in solving boundary layer type of problems as arise in carrier-mediated transport. The method uses an efficient LU decomposition of a blockdiagonal matrix. A residual criterion is used for the placement of elements which can be easily implemented using an interactive feature in the computer program. Numerical results for three different systems; a system with simple kinetics and equal diffusivities for carrier and its complex, a system with simple kinetics and unequal diffusivities and a system with complex kinetics and equal diffusivities, indicate that the method is very versatile and has very good convergence properties. The method can be used very easily for all these systems by making minor modifications to the computer program.