A method of lines approach for modelling saltwater intrusion in coastal aquifers

Tim Moroney, Simon Truscott


The equations governing saltwater intrusion in coastal aquifers are complex. Backward Euler time stepping approaches are often used to advance the solution to these equations in time, which typically requires that small time steps be taken in order to ensure that an accurate solution is obtained. We show that a method of lines approach incorporating variable order backward differentiation formulas can greatly improve the efficiency of the time stepping process.

  • K. Bajracharya, J. Arunakumaren, and W. J. Huxley. Numerical modelling of seawater intrusion in Gooburrum, Bundaberg, Queensland. In T. R. Weaver and C. R. Lawrence, editors, Proceedings, Groundwater: Sustainable Solutions, pages 613ñ--618. University of Melbourne, 1998.
  • J. Bear. Hydraulics of groundwater. McGraw-Hill, New York, 1979.
  • K. E. Brenan, S. L. Campbell, and L. R. Petzold. Numerical solution of initial-value problems in differential-algebraic equations. SIAM, Philadelphia, 1996.
  • Jing-Ru Cheng, Robert O. Strobl, Gour-Tsyh Yeh, Hsin-Chi Lin, and Woo Hee Choi. Modeling of 2D density-dependent flow and transport in the subsurface. J. Hydrologic Eng., 3(4):248--257, 1998. doi:10.1061/(ASCE)1084-0699(1998)3:4(248)
  • A. C. Hindmarsh, P. N. Brown, K. E. Grant, S. L. Lee, R. Serban, D. E. Shumaker, and C. S. Woodward. SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers. ACM Transactions on Mathematical Software, 31(3):363--396, 2005. https://computation.llnl.gov/casc/nsde/pubs/toms_sundials.pdf
  • P. S. Huyakorn, P. F. Andersen, J. W. Mercer, and Jr. H. O. White. Saltwater intrusion in aquifers: Development and testing of a three-dimensional, finite-element model. Water Resources Research, 23(2):293--312, 1987.
  • F. Liu, V. V. Anh, I. Turner, K. Bajracharya, W. J. Huxley, and N. Su. A finite volume simulation model for saturated-unsaturated flow and application to Gooburrum, Bundaberg, Queensland, Australia. Applied Mathematical Modelling, 30(4):352--366, 2006. doi:10.1016/j.apm.2005.05.007
  • M. D. Tocci, C. T. Kelley, and C. T. Miller. Accurate and economical solution of the pressure-head form of richards' equation by the method of lines. Advances In Water Resources, 20(1):1--14, 1997. doi:10.1016/S0309-1708(96)00008-5
  • Q. Zhang, R. E. Volker, and D. A. Lockington. Numerical investigation of seawater intrusion at Gooburrum, Bundaberg, Queensland, Australia. Hydrogeology Journal, 12:674--687, 2004. doi:10.1007/s10040-004-0333-5

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DOI: http://dx.doi.org/10.21914/anziamj.v50i0.1413

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