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

Pages (from-to) | 371-379 |

Number of pages | 9 |

Journal | Developments in Water Science |

Volume | 55 |

Issue number | PART 1 |

DOIs | |

State | Published - 2004 |

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### ASJC Scopus subject areas

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

### Cite this

*Developments in Water Science*,

*55*(PART 1), 371-379. https://doi.org/10.1016/S0167-5648(04)80065-0

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

Research output: Contribution to journal › Article

*Developments in Water Science*, vol. 55, no. PART 1, pp. 371-379. https://doi.org/10.1016/S0167-5648(04)80065-0

}

TY - JOUR

T1 - Laplace transform analytic element method for transient flow problems

AU - Furman, Alex

AU - Neuman, Shlomo P

PY - 2004

Y1 - 2004

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=80051580934&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80051580934&partnerID=8YFLogxK

U2 - 10.1016/S0167-5648(04)80065-0

DO - 10.1016/S0167-5648(04)80065-0

M3 - Article

AN - SCOPUS:80051580934

VL - 55

SP - 371

EP - 379

JO - Developments in Water Science

JF - Developments in Water Science

SN - 0167-5648

IS - PART 1

ER -