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An improved collocation method for solving the Henry problem.

Hrvoje Gotovac1, Roko Andricevic, Blaz Gotovac

  • 1Department of Civil Engineering, University of Split, Matice hrvatske 15, 21000 Split, Croatia.

Journal of Contaminant Hydrology
|May 15, 2003
PubMed
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This study introduces an improved numerical solution for the Henry problem using the Fup Fragment Collocation Method (FFCM). The FFCM accurately models the seepage face, overcoming challenges with the original Henry problem's boundary conditions.

Area of Science:

  • Fluid dynamics
  • Numerical analysis
  • Computational mathematics

Background:

  • The original Henry problem presents numerical challenges due to its severe sea boundary condition.
  • Accurate representation of the seepage face is difficult with fixed sea concentration at the boundary.

Purpose of the Study:

  • To present an improved numerical solution for the Henry problem.
  • To demonstrate the accuracy and robustness of a novel numerical method for fluid flow problems.

Main Methods:

  • The steady-state dimensionless equations are solved using the Fup Fragment Collocation Method (FFCM).
  • R(bf) basis functions of Fup(2) (x, y) type are employed within the FFCM.
  • The method allows for classical formulation and high approximation accuracy.

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Main Results:

  • The FFCM provides an accurate and robust numerical solution for the Henry problem.
  • The method effectively handles the challenges associated with the seepage face and boundary conditions.
  • Comparison with published solutions confirms the high approximation accuracy of the FFCM.

Conclusions:

  • The FFCM is a reliable numerical technique for solving the Henry problem and similar fluid flow scenarios.
  • The improved numerical solution addresses the limitations of previous methods in representing the discharge area.
  • The study validates the FFCM's capability in accurately describing complex boundary conditions in fluid dynamics.