An analysis of groundwater flow in an infinite region with a sinusoidal top

P. N. Shivakumar, Joseph J. Williams, Qiang Ye, Chuanxiang Ji

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


In this paper we give a mathematical analysis with numerical computation for a groundwater flow problem described by an elliptic equation of the form ∇ · (edx∇φ(x, z)) = 0, d ≥ 0 in a semi-infinite vertical region bounded on top by a sloping sinusoidal curve, under given boundary conditions. φ(x, z) represents the hydraulic head and edx represents the relative hydraulic conductivity (or permeability). We reduce the problem to an infinite system of linear equations using the method of separation of variables and construction of a Grammian matrix. Truncation of this system yields an approximate solution that gives the best match on the top boundary. Computational results for some typical parameters are presented.

Original languageEnglish
Pages (from-to)263-271
Number of pages9
JournalNumerical Functional Analysis and Optimization
Issue number1-2
StatePublished - 2000


  • Elliptic PDE
  • Groundwater flow
  • Modified bessel functions

ASJC Scopus subject areas

  • Analysis
  • Signal Processing
  • Computer Science Applications
  • Control and Optimization


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