Laplace transform analytic element method for transient flow problems

Alex Furman, Shlomo P Neuman

Research output: Contribution to journalArticle

Abstract

Recently we [12] proposed a new Laplace transform analytic element method (LT-AEM) for the solution of transient groundwater flow problems. Laplace transformation of the transient flow equations leads to a time-independent modified Helmholtz equation and associated conditions at discontinuities. The latter are solved by AEM and the results transformed numerically back into the time domain. Though neither continuity of potential nor continuity of flux are satisfied automatically at internal discontinuities, both are satisfied approximately via least squares at an overdetermined system of control points in a manner similar to that of Janković [17] and Barnes and Janković [5]. LT-AEM preserves all advantages of the AEM in Laplace space, most importantly its mathematical elegance and grid-free nature. Solution in Laplace space and numerical back transformation into the time domain are done independently for any given time and are thus amenable to parallel computation on multiple processors. This renders the method particularly well suited for cases where a high-accuracy solution is required at a relatively small number of discrete space-time locations. LT-AEM requires a new family of analytic elements associated transformation of known analytic solutions in the time domain, or developed directly in the Laplace domain. We use both methods to develop a number of analytic elements for LT-AEM. We then illustrate the method on transient flow in a two-dimensional confined aquifer containing various inhomogeneities and time-dependent sources.

Original languageEnglish (US)
Pages (from-to)371-379
Number of pages9
JournalDevelopments in Water Science
Volume55
Issue numberPART 1
DOIs
StatePublished - 2004

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Laplace transform
transient flow
Laplace transforms
Helmholtz equation
Groundwater flow
Aquifers
discontinuity
Fluxes
confined aquifer
method
inhomogeneity
groundwater flow

ASJC Scopus subject areas

  • Geotechnical Engineering and Engineering Geology
  • Oceanography
  • Ocean Engineering
  • Mechanical Engineering
  • Water Science and Technology

Cite this

Laplace transform analytic element method for transient flow problems. / Furman, Alex; Neuman, Shlomo P.

In: Developments in Water Science, Vol. 55, No. PART 1, 2004, p. 371-379.

Research output: Contribution to journalArticle

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