TY - JOUR

T1 - Numerical convergence does not mean mathematical convergence

T2 - Examples of simple saturated steady-state groundwater models with pumping wells

AU - Chapuis, Robert P.

AU - Duhaime, François

AU - Weber, Simon

AU - Marefat, Vahid

AU - Zhang, Lu

AU - Blessent, Daniela

AU - Bouaanani, Najib

AU - Pelletier, Dominique

N1 - Funding Information:
This article results from long personal research activities by the authors, who did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
Publisher Copyright:
© 2023 Elsevier Ltd

PY - 2023/10

Y1 - 2023/10

N2 - Groundwater numerical studies do not include H-convergence tests, contrarily to computational fluid dynamics (CFD) studies. In regional groundwater studies with pumping wells, the grids may exceed 106 nodes. The authors examine whether H-convergence tests can help to calculate the numerical errors made by using large grids with element sizes in the 10–500 m range. First, the differences between numerical and mathematical convergences are explained. Then, a method is proposed that most users may easily implement for their groundwater studies to assess the numerical error linked to the element size, ES, and the aspect ratio, AR. A single problem, forming a simple part of a regional groundwater study, was examined and solved by using many uniform grids. The results show that most regional groundwater studies make errors in the 50–500% range, considering their usual values for ES and AR. The numerical convergence domain, NCD, is shown to be larger than the mathematical convergence domain, MCD. This means that the codes can provide a numerical solution for a large range of ES values, even for many values outside the MCD, which is a risky situation for designers who are unaware of the difference between NCD and MCD and ignore the H-convergence tests.

AB - Groundwater numerical studies do not include H-convergence tests, contrarily to computational fluid dynamics (CFD) studies. In regional groundwater studies with pumping wells, the grids may exceed 106 nodes. The authors examine whether H-convergence tests can help to calculate the numerical errors made by using large grids with element sizes in the 10–500 m range. First, the differences between numerical and mathematical convergences are explained. Then, a method is proposed that most users may easily implement for their groundwater studies to assess the numerical error linked to the element size, ES, and the aspect ratio, AR. A single problem, forming a simple part of a regional groundwater study, was examined and solved by using many uniform grids. The results show that most regional groundwater studies make errors in the 50–500% range, considering their usual values for ES and AR. The numerical convergence domain, NCD, is shown to be larger than the mathematical convergence domain, MCD. This means that the codes can provide a numerical solution for a large range of ES values, even for many values outside the MCD, which is a risky situation for designers who are unaware of the difference between NCD and MCD and ignore the H-convergence tests.

KW - Groundwater

KW - Mathematical convergence

KW - Numerical analysis

KW - Numerical convergence

KW - Pumping

UR - http://www.scopus.com/inward/record.url?scp=85164226524&partnerID=8YFLogxK

U2 - 10.1016/j.compgeo.2023.105615

DO - 10.1016/j.compgeo.2023.105615

M3 - Artículo

AN - SCOPUS:85164226524

SN - 0266-352X

VL - 162

JO - Computers and Geotechnics

JF - Computers and Geotechnics

M1 - 105615

ER -