TY - JOUR
T1 - An operator splitting algorithm for coupled one-dimensional advection-diffusion-reaction equations
AU - Khan, Liaqat Ali
AU - Liu, Philip L.F.
N1 - Funding Information:
The research reported in this paper was in part supported by a research grant from the Xerox Corporation to Cornell University. During the course of study LAK has also been supported by a Fellowship from the DeFrees Foundation. This researchw as conducted using the Cornell National SupercomputerF acility, which receivesm ajor funding from the National ScienceF oundation and IBM Corporation, and with additional support from New York State and members of the Corporate Research Institute.
PY - 1995/11
Y1 - 1995/11
N2 - 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 Duhamel's 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.
AB - 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 Duhamel's 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.
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U2 - 10.1016/0045-7825(95)00839-5
DO - 10.1016/0045-7825(95)00839-5
M3 - Article
AN - SCOPUS:0029412989
SN - 0045-7825
VL - 127
SP - 181
EP - 201
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
IS - 1-4
ER -