Application of the decomposition method to the solution of the reaction-convection-diffusion equation

摘要

The nonlinear reaction-convection-diffusion equation, which characterizes the time-dependent advection and dispersion of a chemically reactive material released into a prescribed flow field, is solved using the decomposition method. The decomposition method provides a means of computing an approximate solution to the problem without the need for an explicit discretization of the partial differential equation. Furthermore, it is shown that in the case of the advection and diffusion of a chemically inert material, the components in the approximate solution can be evaluated analytically. Consequently, in this case, the decomposition method can be readily implemented using computer algebra. The efficacy and accuracy of the solution, obtained by application of the decomposition method, are evaluated by comparison to a known exact solution for the case of the dispersion of a chemically inert material in a linear shear flow field.