A Dirac-delta function notation for source/sink terms in groundwater flow
JOURNAL OF HYDROLOGIC ENGINEERING, vol.10, no.5, pp.420-427, 2005 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 10 Issue: 5
- Publication Date: 2005
- Doi Number: 10.1061/(asce)1084-0699(2005)10:5(420)
- Journal Name: JOURNAL OF HYDROLOGIC ENGINEERING
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.420-427
- Dokuz Eylül University Affiliated: No
Abstract
The source/sink terms in groundwater flow are singularities that require special treatment in the numerical solution of a mathematical model. Except for the case of a point source, these singularities are not consistently defined in the governing partial differential equation or treated rigorously in the numerical solution of the governing equations. In this paper, we propose a consistent notation for handling the source/sink terms within the governing equation using the familiar Dirac-delta function notation for three-dimensional applications. We also present the domain integrals of these terms, similar to the ones that occur frequently in finite element solution of the mathematical model.