### 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 language | English (US) |
---|---|

Pages (from-to) | 113-130 |

Number of pages | 18 |

Journal | Journal of Engineering Mathematics |

Volume | 64 |

Issue number | 2 |

DOIs | |

State | Published - 2009 |

### Fingerprint

### 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

*Journal of Engineering Mathematics*,

*64*(2), 113-130. https://doi.org/10.1007/s10665-008-9251-1

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

Research output: Contribution to journal › Article

*Journal of Engineering Mathematics*, vol. 64, no. 2, pp. 113-130. https://doi.org/10.1007/s10665-008-9251-1

}

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

VL - 64

SP - 113

EP - 130

JO - Journal of Engineering Mathematics

JF - Journal of Engineering Mathematics

SN - 0022-0833

IS - 2

ER -