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Assessment of a non-traditional operator split algorithm for simulation of reactive transport

Author

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  • Simpson, Matthew J.
  • Landman, Kerry A.
  • Clement, T.Prabhakar

Abstract

A non-traditional operator split (OS) scheme for the solution of the advection-diffusion-reaction (ADR) equation is proposed. The scheme is implemented with the recently published central scheme [A. Kurganov, E. Tadmor, New high-resolution central schemes for non-linear conservation laws and convection-diffusion equations, J. Comput. Phys. 160 (2000) 241–282] to accurately simulate advection-reaction processes. The governing partial differential equation (PDE) is split into two PDEs, which are solved sequentially within each time step. Unlike traditional methods, the proposed scheme provides a very efficient method to solve the ADR equation for any value of the grid-Péclet number. An analytical mass balance error analysis shows that the proposed non-traditional scheme incurs a splitting error, which behaves differently to the splitting error incurred in traditional OS schemes. Numerical results are presented to illustrate the robustness of the proposed scheme.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:70:y:2005:i:1:p:44-60
    DOI: 10.1016/j.matcom.2005.03.019
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    References listed on IDEAS

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    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. 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.
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    Cited by:

    1. 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.
    2. Baker, Ruth E. & Simpson, Matthew J., 2012. "Models of collective cell motion for cell populations with different aspect ratio: Diffusion, proliferation and travelling waves," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(14), pages 3729-3750.
    3. Katrina K Treloar & Matthew J Simpson, 2013. "Sensitivity of Edge Detection Methods for Quantifying Cell Migration Assays," PLOS ONE, Public Library of Science, vol. 8(6), pages 1-10, June.

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    1. 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.
    2. 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.

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