An operator splitting algorithm for coupled one-dimensional advection-diffusion-reaction equations Original Research Article

An operator splitting algorithm for a system of one-dimensional advection-diffusion-reaction equations, describing the transport of non-conservative pollutants, is presented in this paper. The algorithm is a Strang type splitting procedure incorporating contributions from the inhomogeneous terms by the Duhamelʹs principle. The associated homogeneous equations are split into advection, diffusion and reaction equations, and solved by a backward method of characteristic, a finite-element method and an explicit Runge-Kutta method, respectively. The boundary conditions applicable to the split equations are derived. Numerical analyses of the algorithm, consisting of the stability, the accuracy and the convergence of the solution procedure, are presented. The composite algorithm is second-order accurate in time and space and conditionally stable. The numerical characteristics of the algorithm are demonstrated by several examples.