Laplace-transform analytic-element method for transient porous-media flow

Kristopher L. Kuhlman, Shlomo P Neuman

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

A unified theory of the Laplace-transform analytic-element method (LT-AEM) for solving transient porous-media flow problems is presented. LT-AEM applies the analytic-element method (AEM) to the modified Helmholtz equation, the Laplace-transformed diffusion equation. LT-AEM uses superposition and boundary collocation with Laplace-space convolution to compute flexible semi-analytic solutions from a small collection of fundamental elements. The elements discussed are derived using eigenfunction expansions of element shapes in their natural coordinates. A new formulation for a constant-strength line source is presented in terms of elliptical coordinates and complex-parameter Mathieu functions. Examples are given illustrating how leaky and damped-wave hydrologic problems can be solved with little modification using existing LT-AEM techniques.

Original languageEnglish (US)
Pages (from-to)113-130
Number of pages18
JournalJournal of Engineering Mathematics
Volume64
Issue number2
DOIs
StatePublished - 2009

Fingerprint

Porous Media Flow
Transient Flow
Laplace transforms
Laplace transform
Porous materials
Helmholtz equation
Mathieu Functions
Convolution
Eigenvalues and eigenfunctions
Eigenfunction Expansion
Modified Equations
Helmholtz Equation
Laplace's equation
Collocation
Laplace
Analytic Solution
Diffusion equation
Damped
Superposition
Formulation

Keywords

  • Analytic element
  • Diffusion equation
  • Elliptical coordinates
  • Laplace transform
  • Mathieu functions
  • Modified Helmholtz equation
  • Transient line source

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

Cite this

Laplace-transform analytic-element method for transient porous-media flow. / Kuhlman, Kristopher L.; Neuman, Shlomo P.

In: Journal of Engineering Mathematics, Vol. 64, No. 2, 2009, p. 113-130.

Research output: Contribution to journalArticle

@article{22ecb4989ae44cbf800360a1951a36e6,
title = "Laplace-transform analytic-element method for transient porous-media flow",
abstract = "A unified theory of the Laplace-transform analytic-element method (LT-AEM) for solving transient porous-media flow problems is presented. LT-AEM applies the analytic-element method (AEM) to the modified Helmholtz equation, the Laplace-transformed diffusion equation. LT-AEM uses superposition and boundary collocation with Laplace-space convolution to compute flexible semi-analytic solutions from a small collection of fundamental elements. The elements discussed are derived using eigenfunction expansions of element shapes in their natural coordinates. A new formulation for a constant-strength line source is presented in terms of elliptical coordinates and complex-parameter Mathieu functions. Examples are given illustrating how leaky and damped-wave hydrologic problems can be solved with little modification using existing LT-AEM techniques.",
keywords = "Analytic element, Diffusion equation, Elliptical coordinates, Laplace transform, Mathieu functions, Modified Helmholtz equation, Transient line source",
author = "Kuhlman, {Kristopher L.} and Neuman, {Shlomo P}",
year = "2009",
doi = "10.1007/s10665-008-9251-1",
language = "English (US)",
volume = "64",
pages = "113--130",
journal = "Journal of Engineering Mathematics",
issn = "0022-0833",
publisher = "Springer Netherlands",
number = "2",

}

TY - JOUR

T1 - Laplace-transform analytic-element method for transient porous-media flow

AU - Kuhlman, Kristopher L.

AU - Neuman, Shlomo P

PY - 2009

Y1 - 2009

N2 - A unified theory of the Laplace-transform analytic-element method (LT-AEM) for solving transient porous-media flow problems is presented. LT-AEM applies the analytic-element method (AEM) to the modified Helmholtz equation, the Laplace-transformed diffusion equation. LT-AEM uses superposition and boundary collocation with Laplace-space convolution to compute flexible semi-analytic solutions from a small collection of fundamental elements. The elements discussed are derived using eigenfunction expansions of element shapes in their natural coordinates. A new formulation for a constant-strength line source is presented in terms of elliptical coordinates and complex-parameter Mathieu functions. Examples are given illustrating how leaky and damped-wave hydrologic problems can be solved with little modification using existing LT-AEM techniques.

AB - A unified theory of the Laplace-transform analytic-element method (LT-AEM) for solving transient porous-media flow problems is presented. LT-AEM applies the analytic-element method (AEM) to the modified Helmholtz equation, the Laplace-transformed diffusion equation. LT-AEM uses superposition and boundary collocation with Laplace-space convolution to compute flexible semi-analytic solutions from a small collection of fundamental elements. The elements discussed are derived using eigenfunction expansions of element shapes in their natural coordinates. A new formulation for a constant-strength line source is presented in terms of elliptical coordinates and complex-parameter Mathieu functions. Examples are given illustrating how leaky and damped-wave hydrologic problems can be solved with little modification using existing LT-AEM techniques.

KW - Analytic element

KW - Diffusion equation

KW - Elliptical coordinates

KW - Laplace transform

KW - Mathieu functions

KW - Modified Helmholtz equation

KW - Transient line source

UR - http://www.scopus.com/inward/record.url?scp=67349139124&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67349139124&partnerID=8YFLogxK

U2 - 10.1007/s10665-008-9251-1

DO - 10.1007/s10665-008-9251-1

M3 - Article

AN - SCOPUS:67349139124

VL - 64

SP - 113

EP - 130

JO - Journal of Engineering Mathematics

JF - Journal of Engineering Mathematics

SN - 0022-0833

IS - 2

ER -