Convergence of iterative split-operator approaches for approximating nonlinear reactive transport problems

✍ Scribed by Joseph F. Kanney; Cass T. Miller; C.T. Kelley

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 187 KB
• Volume: 26
• Category: Article
• ISSN: 0309-1708
• DOI: 10.1016/s0309-1708(02)00162-8

✦ Synopsis

Numerical solutions to nonlinear reactive solute transport problems (NRTPs) are often computed using split-operator (SO) approaches, which separate the transport and reaction processes. This uncoupling introduces an additional source of numerical error, known as the splitting error. The iterative split-operator (ISO) algorithm removes the splitting error through iteration. Although the ISO algorithm is often used, there has been very little analysis of its convergence behavior. This work uses theoretical analysis and numerical experiments to investigate the convergence rate of the ISO approach for solving NRTPs. We show that under certain assumptions regarding smoothness, the convergence rate of the ISO algorithm applied NRTPs is OðDt 2 Þ. We demonstrate that the theoretical convergence rate can be achieved in practice if the numerical solution of the transport and reaction steps are carried out with sufficient accuracy. We also show that accurate estimation of the lagged operator in each step is crucial to obtaining the theoretical convergence rate.