Asymptotic expansions for Moench’s integral transform of hydrology

López, José L. ; Pagola, Pedro ; Pérez Sinusía, Ester (Universidad de Zaragoza)

Resumen: Theis’ theory (1935), later improved by Hantush & Jacob (1955) and Moench (1971), is a technique designed to study the water level in aquifers. The key formula in this theory is a certain integral transform H[g](r,t) of the pumping function g that depends on the time t and the relative position r to the pumping point as well as on other physical parameters. Several analytic approximations of H[g](r,t) have been investigated in the literature that are valid and accurate in certain regions of r, t and the mentioned physical parameters. In this paper, the analysis of possible analytic approximations of H[g](r,t) is completed by investigating asymptotic expansions of H[g](r,t) in a region of the parameters that is of interest in practical situations, but that has not yet been investigated. Explicit and/or recursive algorithms for the computation of the coefficients of the expansions and estimates for the remainders are provided. Some numerical examples based on an actual physical experiment conducted by Layne-Western Company in 1953 illustrate the accuracy of the approximations.

Idioma: Inglés

DOI: 10.3390/math11143053

Año: 2023

Publicado en: Mathematics 11, 14 (2023), 3053 [14 pp.]
ISSN: 2227-7390

Factor impacto JCR: 2.3 (2023)

Categ. JCR: MATHEMATICS rank: 21 / 490 = 0.043 (2023) - Q1 - T1

Factor impacto CITESCORE: 4.0 - Mathematics (all) (Q1) - Engineering (miscellaneous) (Q2) - Computer Science (miscellaneous) (Q2)

Factor impacto SCIMAGO: 0.475 - Engineering (miscellaneous) (Q2) - Mathematics (miscellaneous) (Q2) - Computer Science (miscellaneous) (Q2)

Tipo y forma: Artículo (Versión definitiva)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)