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Analysis of split operator methods for nonlinear and multispecies groundwater chemical transport models

Author

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  • Barry, D.A.
  • Miller, C.T.
  • Culligan, P.J.
  • Bajracharya, K.

Abstract

Coupled solute transport and reaction models are computationally demanding when multispecies, multidimensional simulations are considered. Split operator methods provide approximate solutions to the reactive solute transport problem that are both relatively efficient to compute and to construct. The transport and reaction operators are split into two separate computational steps. Split operator methods are introduced in the context of single species sorption to the soil, with an emphasis on the splitting errors that are induced. For standard two-step methods, the splitting error is proportional to Δt, the temporal step size of the numerical scheme. The alternating split operator scheme, in which the order of the operations is switched at succeeding time steps, apparently does not remove the splitting error for nonlinear reactions, whereas it is removed for linear cases. The truncation error is extended to the case of two reacting species.

Suggested Citation

  • Barry, D.A. & Miller, C.T. & Culligan, P.J. & Bajracharya, K., 1997. "Analysis of split operator methods for nonlinear and multispecies groundwater chemical transport models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 43(3), pages 331-341.
    • Handle: RePEc:eee:matcom:v:43:y:1997:i:3:p:331-341
    DOI: 10.1016/S0378-4754(97)00017-7
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    Cited by:

    1. Barry, D.A. & Bajracharya, K. & Crapper, M. & Prommer, H. & Cunningham, C.J., 2000. "Comparison of split-operator methods for solving coupled chemical non-equilibrium reaction/groundwater transport models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 53(1), pages 113-127.
    2. Simpson, Matthew J. & Landman, Kerry A. & Clement, T.Prabhakar, 2005. "Assessment of a non-traditional operator split algorithm for simulation of reactive transport," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 70(1), pages 44-60.
    3. Simpson, Matthew J. & Landman, Kerry A., 2008. "Theoretical analysis and physical interpretation of temporal truncation errors in operator split algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(1), pages 9-21.

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