NDLI: Numerical modeling of Forchheimer flow to a pumping well in a confined aquifer using the strong-form mesh-free method

Content Provider	Springer Nature Link
Author	Wen, Zhang Liu, Zhuangtian Jin, Menggui Zhan, Hongbin
Copyright Year	2014
Abstract	A numerical analysis of non-Darcian flow to a pumping well in a confined aquifer using the strong-form mesh-free (MFREE) method is described. This technique is targeted at problems that use advanced numerical approaches for modeling non-Darcian flow and it supports the assumption that the non-Darcian flow follows the Forchheimer equation. Interpolation functions including the multi-quadrics (MQ) basis function (containing shape factors q and α) and the Gaussian (EXP) basis function (with shape factor ω) were found to be important defining parameters which had significant influence on the numerical results. A series of numerical experiments revealed that when q = 2 and α = 0.1, the mesh-free method yielded good results and the range of 10$^{−6}$ – 10$^{−3}$ might be a good choice for the shape factor ω in the EXP basis function. A comparison between the strong-form MFREE method and the finite difference method was done; the results showed that the strong-form MFREE method was very effective for solving non-Darcian flow near a pumping well in a confined aquifer, and was favorable over the finite-difference method, which could undergo oscillation and converging problems at early times.Une analyse numérique d’un écoulement non darcien au niveau d’un puits de pompage dans un aquifère captif en utilisant la méthode robuste de forme sans maille (MRFM) est décrite. Cette technique est dédiée aux problèmes qui utilisent des approches numériques avancées pour la modélisation des écoulements non darciens et soutient l’hypothèse que les écoulements non darciens suivent l’équation de Forchheimer. Les fonctions d’interpolation comprenant la fonction de base multi-quadrique(MQ) (contenant les facteurs de forme q et α) et la fonction Gaussienne (EXP) (avec un facteur de forme ω) ont été jugées comme étant des paramètres importants qui ont une influence significative sur les résultats numériques. Une série d’expériences numériques a révélé que lorsque q = 2 et α = 0.1, la méthode sans maille donne de bons résultats et la gamme de 10$^{−6}$ ∼ 10$^{−3}$ pourrait être un bon choix pour le facteur de forme ω de la fonction EXP. Une comparaison entre la méthode robuste de forme sans maille (MRFM) et la méthode des différences finies a été réalisée; les résultats ont montré que la méthode sans maille MRFM était très efficace pour résoudre les écoulements non darciens à proximité du puits de pompage situé dans un aquifère captif, et qu’elle était préférable à la méthode des différences finies, qui pourrait occasionner des oscillations et des problèmes de convergence dès le début des simulations.Se describe el análisis numérico de un flujo no Darciano hacia un pozo de bombeo en un acuífero no confinado usando el método de formas fuertes sin malla (MFREE). Esta técnica está dirigida a problemas que usan enfoques numéricos avanzados para modelar el flujo no Darciano y se apoya en la suposición que el flujo no Darciano sigue la ecuación de Forchheimer. Se encontró que las funciones de interpolación que incluyen las funciones de base multicuádricas (MQ) (que contienen factores de forma q y α) y la funciones de base Gaussianas (EXP) (con factor de forma ω) son importantes parámetros de definición que tienen influencia en los resultados numéricos. Una serie de experimentos numéricos revelaron que cuando q = 2 y α = 0.1, el método sin malla dio buenos resultados y que el intervalo 10$^{−6}$ ∼ 10$^{−3}$ podría ser una buena elección para el factor de forma ω en la función de base EXP. Se realizó una comparación entre el método de formas fuertes MFREE y el método de diferencias finitas, los resultados mostraron que el método de formas fuertes era muy efectivo para resolver el flujo no Darciano cerca a un pozo de bombeo en un acuífero confinado, y resultó favorable sobre el método de diferencias finitas, el cual puede sobrellevar problemas de oscilación y convergencia en los primeros tiempos.本文采用无网格强式法求解了承压含水层中抽水井附近非达西渗流模型,假设非达西渗流能够采用Forchheimer方程进行描述,本文旨在介绍无网格这种新兴数值方法求解非达西渗流问题。本文分别采用多项式插值函数以及指数插值函数进行了系列数值试验,研究结果发现多项式插值函数中的两个形状参数(q和α)和指数插值函数中的形状参数ω对数值模拟结果影响较大。当多项式插值函数中的形状参数q = 2和α = 0.1能得到较好的结果,而指数插值函数中的形状参数ω选择区间较大,在10$^{−6}$ ∼ 10$^{−3}$的范围内均能得到较好的结果。本文将无网格强式法和有限差分方法进行了比较,结果表明无网格强式法在求解此类非达西渗流模型是非常有效的,在抽水初期有限差分方法可能会导致数值震荡问题,而无网格强式法能避免此类问题。Descreve-se a análise numérica do fluxo não-Darciano em direção a um furo de bombeamento num aquífero confinado, através do método de forma robusta sem malha (MFREE). Esta técnica aplica-se a problemas que usam métodos numéricos avançados para modelar fluxo não-Darciano e é capaz de lidar com o pressuposto de que o fluxo não-Darciano segue a equação de Forchheimer. Constatou-se que as equações de interpolação, incluindo a função de base multi-quadrática (MQ, com fatores de forma q e α) e a função de base Gaussiana (EXP, com o fator de forma ω), são importantes para definir parâmetros que têm uma influência significativa nos resultados numéricos. Um conjunto de experiências numéricas revelou que quando q = 2 e α = 0.1, o método sem malha conduziu a bons resultados e a gama de 10$^{−6}$ ∼ 10$^{−3}$ pode ser uma boa escolha para o fator de forma ω na função de base EXP. Foi feita uma comparação entre o método de forma robusta MFREE e o método de diferenças finitas; os resultados indicam que o método de forma robusta MFREE foi muito eficiente a resolver fluxo não-Darciano nas imediações do furo de bombeamento num aquífero confinado, e revelou-se favorável face ao método das diferenças finitas, uma vez que este podia sofrer oscilações e problemas de convergência nos tempos iniciais.
Starting Page	1207
Ending Page	1215
Page Count	9
File Format	PDF
ISSN	14312174
Journal	Hydrogeology Journal
Volume Number	22
Issue Number	5
e-ISSN	14350157
Language	Portuguese
Publisher	Springer Berlin Heidelberg
Publisher Date	2014-05-29
Publisher Institution	International Association of Hydrogeologists
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Groundwater flow Numerical modeling Mesh-free method Forchheimer equation Point interpolation Hydrogeology Hydrology/Water Resources Geology Waste Water Technology Water Pollution Control Water Management Aquatic Pollution
Content Type	Text
Resource Type	Article
Subject	Earth and Planetary Sciences Water Science and Technology

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Non-Darcian flow to a well in a leaky aquifer using the Forchheimer equation

Regional groundwater flow modeling of the Geba basin, northern Ethiopia

MODFLOW procedure to simulate axisymmetric flow in radially heterogeneous and layered aquifer systems

Effects of regional groundwater flow on the performance of an aquifer thermal energy storage system under continuous operation

Identifying watershed-scale groundwater flow barriers: the Yoqne’am Fault in Israel

Groundwater response to tidal fluctuations in wedge-shaped confined aquifers

Evaluation of a pumping test of the Snake River Plain aquifer using axial-flow numerical modeling

How basin model results enable the study of multi-layer aquifer response to pumping: the Paris Basin, France

Top-down groundwater hydrograph time-series modeling for climate-pumping decomposition

Numerical modeling of Forchheimer flow to a pumping well in a confined aquifer using the strong-form mesh-free method

Similar Documents

Non-Darcian flow to a well in a leaky aquifer using the Forchheimer equation

Regional groundwater flow modeling of the Geba basin, northern Ethiopia

MODFLOW procedure to simulate axisymmetric flow in radially heterogeneous and layered aquifer systems

Effects of regional groundwater flow on the performance of an aquifer thermal energy storage system under continuous operation

Identifying watershed-scale groundwater flow barriers: the Yoqne’am Fault in Israel

Groundwater response to tidal fluctuations in wedge-shaped confined aquifers

Evaluation of a pumping test of the Snake River Plain aquifer using axial-flow numerical modeling

How basin model results enable the study of multi-layer aquifer response to pumping: the Paris Basin, France

Top-down groundwater hydrograph time-series modeling for climate-pumping decomposition

Numerical modeling of Forchheimer flow to a pumping well in a confined aquifer using the strong-form mesh-free method