Critical assessment of the operator-splitting technique in solving the advection-dispersion-reaction equation: 2. Monod kinetics and coupled transport

Morshed, Jahangir; Kaluarachchi, Jagath J.

doi:10.1016/0309-1708(95)00002-z

Cited by 29 publications

(11 citation statements)

References 8 publications

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“…Barry et al showed that the splitting error of the ASO algorithm is O ∆t 2 for ADRE's with linear reactions [7], but that this result does not hold for nonlinear reactions [5]. Subsequent analysis of SSO and ASO applied to linear and nonlinear ADRE's [28,47] confirmed earlier results [5,7,6,70] and highlighted the dependence of the splitting error on the magnitude of the reaction rates.…”

Section: Error Analysismentioning

confidence: 68%

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

Kanney

Miller

Kelley

2003

Advances in Water Resources

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Numerical solutions to nonlinear reactive solute transport problems 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 iterative split-operator approach for solving nonlinear reactive transport problems.

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Section: Error Analysismentioning

confidence: 68%

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

Kanney

Miller

Kelley

2003

Advances in Water Resources

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“…As a result, signiÿcant numerical errors occur around these locations [25,26]. On the other hand, the use of will provide exact concentrations on the Type I (Dirichlet) boundary and accurate estimations on the Type III (Cauchy) boundary when advection is the dominating transport process.…”

Section: Predictor-corrector (Pc) Techniquementioning

confidence: 98%

“…The OS technique has been studied and assessed by many researchers using the conventional Eulerian (CE) approach [24][25][26]. Their results showed that the regular OS technique yielded very deviated results near the upstream boundary (up to 60% concentration prediction error); the modiÿed alternate operator-splitting (AOS) technique could e ectively reduce such an error only at even time steps (up to about 10%) but still yielded signiÿcant errors at odd time steps (up to 30%).…”

Section: Introductionmentioning

confidence: 96%

An assessment of using the predictor–corrector technique to solve reactive transport equations

Cheng

2002

Numerical Meth Engineering

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SUMMARYWe examined, through comparison among the full-coupling (FC), operator-splitting (OS), and predictorcorrector (PC) techniques, the e ectiveness of using the PC technique to solve depth-averaged reactive transport equations in the shallow water domain. Our investigation has led to three major conclusions. Firstly, both the OS and PC techniques can e ciently solve reactive transport equations because the advection-di usion transport equations are solved outside the non-linear iteration loop and the reaction equations are solved node by node. However, these two techniques may risk sacriÿcing computational accuracy. Secondly, the OS or PC technique incorporated with the Lagrangian-Eulerian (LE) approach can handle boundary sources more precisely than alternatively with the conventional Eulerian (CE) approach. Thirdly, with the LE approach incorporated, the numerical results from the three techniques agreed highly with one another except when di usion became signiÿcant. In this case, the PC technique's result still matched well with the FC technique's result, but di erences between the OS and FC techniques' results arose as di usion increased. Based on this study, we recommend to apply as a ÿrst step the PC technique to solving reactive transport equations with respect to both computational e ciency and accuracy.

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“…Several investigators have analyzed the splitting error to advectiondispersion-reaction simulations (Valocchi and Malmstead 1992;Kaluarachchi and Morshed 1995;Morshed and Kaluarachchi 1995;Barry et al 1996aBarry et al , 1996bBarry et al , 2000Lanser and Verwer 1999;Carrayrou et al 2004). To avoid or reduce the splitting error, several techniques have been developed (e.g., Lanser and Verwer 1999;Simpson et al 2005), but they come with an additional computation effort.…”

Section: Introductionmentioning

confidence: 99%

Modeling reactive transport using exact solutions for first-order reaction networks

Sun

Buscheck

2007

Transp Porous Med

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Operator splitting is often used for solving advection-dispersion-reaction (ADR) equations. Each operator can be solved separately using an algorithm appropriate to its mathematical behavior. Although a lot of research has been done in operator splitting for solving ADR equations, numerical approaches for the reaction operator are computationally expensive. To meet the convergence criteria of ODE (ordinary differential equation) or DAE (differential algebraic equation) solvers, a transport time step has to be subdivided into a large number of reaction time steps. Additional computation effort is also required to reduce the splitting error. In this paper, we develop exact solutions of various first-order reaction networks for the reaction operator and couple those solutions with numerical solutions of the transport operator. The reactions are treated as local phenomena and simulated using exact solutions that we develop, while advection and dispersion are treated as global processes and simulated numerically. The proposed method avoids the numerical error from the reaction operator and requires a single-step calculation to solve the reaction operator. Compared to conventional operator-splitting methods, the proposed method offers both computational efficiency and simulation accuracy.

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Critical assessment of the operator-splitting technique in solving the advection-dispersion-reaction equation: 2. Monod kinetics and coupled transport

Cited by 29 publications

References 8 publications

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

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

An assessment of using the predictor–corrector technique to solve reactive transport equations

Modeling reactive transport using exact solutions for first-order reaction networks

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