Premium
Finite Analytic Numerical Solution for Two‐Dimensional Groundwater Solute Transport
Author(s) -
Hwang Jack C.,
Chen ChingJen,
Sheikhoslami M.,
Panigarahi Bijay K.
Publication year - 1985
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr021i009p01354
Subject(s) - tridiagonal matrix , mathematics , finite element method , tridiagonal matrix algorithm , numerical analysis , matrix (chemical analysis) , péclet number , analytic element method , finite difference , finite difference method , dispersion (optics) , algebraic equation , partial differential equation , mathematical analysis , physics , mechanics , thermodynamics , optics , eigenvalues and eigenvectors , materials science , quantum mechanics , nonlinear system , composite material
A new numerical method called the finite analytic (FA) method is used to solve a groundwater solute transport problem. The basic idea of the finite analytic method is the incorporation of local analytic solution in the numerical solution of the partial differential equation. When the local analytic solution is evaluated at a given nodal point, it gives an algebraic relationship between a nodal value in an element and its neighboring nodal points. The assemble of the linear system equations results in a tridiagonal matrix. Like most finite difference method, the advantages of using efficient iterative techniques for solving tridiagonal matrices are equally applicable to FA method. The automatic localized upstream shift and the analytic property of the FA method eliminates the difficulty of numerical dispersion locally and suppresses the overall numerical dispersion for large Peclet number. For small Peclet number FA method yields excellent results in comparison with the analytic solution. For large Peclet number FA solutions are oscillation free with some degree of numerical dispersion. The results are comparable with those obtained using upstream weighted finite element method.