A comparison of some numerical methods in solving 1-D steady-state advection dispersion reaction equation: Fid-Bau Portal

A comparison of some numerical methods in solving 1-D steady-state advection dispersion reaction equation

Yudianto, D. / Yuebo, Xie

This article is devoted to giving comprehensive description about some numerical schemes in solving 1-D transport and reaction differential equation under steady-state condition. The schemes used include the finite difference method, the shooting method, and the collocation method. Besides those schemes, this article also provides brief review of the continually stirred tank reactors (CSTRs) approach compared with the partial differential equations (PDEs) model that makes use of pdepe solver function of MATLAB. Based on the results obtained, it is shown that the finite difference method is less accurate compared with other methods, especially when the Dirichlet condition is applied. When Neumann condition is used, however, all schemes show almost similar accuracy for small step sizes. Although the CSTRs system generally results in error three to four times greater than PDEs model for the same grid spacing, its inaccuracy can be lowered by increasing the number of cells. Moreover, a simple application in developing dissolved oxygen sag curve for nontidal large river or estuary has strongly offered another possibility of pdepe solver to be used in either teaching-learning processes or even further applications in water quality modelling.