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Multi-resolution adaptive modeling of groundwater flow and transport problems
KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering.
Univ. Split.
Univ. Split.
2007 (English)In: Advances in Water Resources, ISSN 0309-1708, E-ISSN 1872-9657, Vol. 30, 1105-1126 p.Article in journal (Refereed) Published
Abstract [en]

Many groundwater flow and transport problems, especially those with sharp fronts, narrow transition zones, layers and fingers, require extensive computational resources. In this paper, we present a novel multi-resolution adaptive Fup approach to solve the above mentioned problems. Our numerical procedure is the Adaptive Fup Collocation Method (AFCM), based on Fup basis functions and designed through a method of lines (MOL). Fup basis functions are localized and infinitely differentiable functions with compact support and are related to more standard choices such as splines or wavelets. This method enables the adaptive multi-reso In tion approach to solve problems with different spatial and temporal scales with a desired level of accuracy using the entire family of Fup basis functions. In addition, the utilized collocation algorithm enables the mesh free approach with consistent velocity approximation and flux continuity due to properties of the Fup basis functions. The introduced numerical procedure was tested and verified by a few characteristic groundwater flow and transport problems, the Buckley-Leverett multiphase flow problem, the 1-D vertical density driven problem and the standard 2-D seawater intrusion benchmark-Henry problem. The results demonstrate that the method is robust and efficient particularly when describing sharp fronts and narrow transition zones changing in space and time.

Place, publisher, year, edition, pages
2007. Vol. 30, 1105-1126 p.
Keyword [en]
Fup basis functions, compact support, method of lines, adaptive Fup collocation method, multi-resolution approach, numerical dispersion, groundwater flow and transport problems
National Category
Civil Engineering
Identifiers
URN: urn:nbn:se:kth:diva-10644DOI: 10.1016/j.advwatres.2006.10.007ISI: 000246092800006Scopus ID: 2-s2.0-33847309618OAI: oai:DiVA.org:kth-10644DiVA: diva2:222635
Note
QC 20100714Available from: 2009-06-09 Created: 2009-06-09 Last updated: 2017-12-13Bibliographically approved
In thesis
1. A multi-resolution approach for modeling flow and solute transport in heterogeneous porous media
Open this publication in new window or tab >>A multi-resolution approach for modeling flow and solute transport in heterogeneous porous media
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Subsurface processes are usually characterized by rare field experiments, sparse measurements,multi-resolution interpretations, stochastic description, related uncertainties and computational complexity. Over the last few decades, different computational techniques and strategies have become indispensable tools for flow and solute transport prediction in heterogeneous porousmedia. This thesis develops a multi-resolution approach based on Fup basis functions with compactsupport, enabling the use of an efficient and adaptive procedure, closely related to currentunderstood physical interpretation. All flow and transport variables, as well as intrinsic heterogeneity,are described in a multi-resolution representation, in the form of a linear combination ofFup basis functions. Each variable is represented on a particular adaptive grid with a prescribedaccuracy. The methodology is applied to solving problems with sharp fronts, and to solving flowand advective transport in highly heterogeneous porous media, under mean uniform flow conditions.The adaptive Fup collocation method, through the well known method of lines, efficientlytracks solutions with sharp fronts, resolving locations and frequencies at all spatial and/or temporalscales. The methodology yields continuous velocity fields and fluxes, enabling accurate andreliable transport analysis. Analysis of the advective transport proves the robustness of the firstordertheory for low and mild heterogeneity. Moreover, due to the accuracy of the improved Monte-Carlo methodology, this thesis presents the effects of high heterogeneity on ensembleflow and travel time statistics. The difference between Eulerian and Lagrangian velocity statisticsand the importance of higher travel time moments are indicative of high heterogeneity. The thirdtravel time moment mostly describes a peak and late arrivals, while higher moments are requiredfor early arrivals which are linked with the largest uncertainty. A particular finding is the linearityof all travel time moments, which implies that in the limit an advective transport in multi-Gaussian field becomes Fickian. By comparison, the transverse displacement pdf converges to aGaussian distribution around 20 integral scales after injection, even for high heterogeneity. Thecapabilities of the presented multi-resolution approach, and the quality of the obtained results,open new areas for further research.

Abstract [sv]

Markprocesser karakteriseras ofta av fåtaliga fältexperiment, glesa mätningar, heterogenitet påolika skalor, slumpmässighet och relaterade osäkerheter, samt beräkningsmässiga svårigheter.Under de senaste årtiondena har olika beräkningstekniker och strategier blivit ovärderliga verktygför att förutspå vattenflöde och ämnestransport i heterogena porösa medier. Denna doktorsavhandling utvecklar ett angreppssätt med flerskaliga upplösningar baserat på Fup basis funktionermed kompakt stöd, som möjliggör en effektiv och anpassningsbar procedur, nära relaterad tillrådande fysiska tolkningar. Alla flödes- och transportvariabler, så väl som heterogeniteten, beskrivsav en flerskaligt upplöst representation, i form av linjära kombinationer av Fup basis funktioner.Varje variabel representeras på ett speciellt anpassningsbar gridnät med given noggrannhet.Metoden appliceras för att lösa problem med skarpa fronter, samt vattenflöde och advektivämnestransport i starkt heterogena porösa medier. Adaptive Fup collocation metoden tillsammansmed den välkända Method of lines, spårar effektivt lösningar med skarpa fronter och löserupp positioner och frekvenser på alla rums- och/eller tidsskalor. Metoden ger kontinuerliga hastighetsfältoch flöden, och möjliggör noggrann och tillförlitlig transportanalys. Analys av advektivtransport understöder stabiliteten i första-ordningens transport teori för låg och mild heterogenitet.Utöver detta, som resultat av noggrannheten i den förbättrade Monte-Carlo metodiken, visardenna avhandling effekten av hög heterogenitet på ensemble statistiken för flöden och transporttider.Skillnaden mellan Eulerisk och Lagrangian hastighetsstatistik och betydelsen av högrestatistiska moment för transporttider, indikerar hög heterogenitet. Det tredje transporttidsmomentetbeskriver huvudsakligen sannolikhetspiken och de långa transporttiderna, medan högremoment behövs för de korta transporttiderna, som har den största osäkerheten. En speciell upptäcktär linjäariteten i transporttidsmoment, som indikerar att advektiv transport i multi-Gaussiska fält blir Gaussisk i gränsen. Som jämförelse konvergerar sannolikhetsfunktioner förden transversella transportförflyttningen mot en Gaussisk fördelning vid runt 20 korrelationslängder efter injektion, även för hög heterogenitet. Förmågan i det presenterade angreppssättet med flerskalig upplösning, och resultatens noggrannhet, öppnar nya områden för fortsatt forskning.

Place, publisher, year, edition, pages
Stockholm: KTH, 2009. xiv, 51 p.
Series
Trita-LWR. PHD, ISSN 1650-8602 ; 1051
Keyword
Multi-resolution adaptive approach; Atomic and Fup basis functions; Monte- Carlo method; Heterogeneous porous media; Flow; Transport; Travel time
National Category
Water Engineering
Identifiers
urn:nbn:se:kth:diva-10655 (URN)978-91-7415-377-4 (ISBN)
Public defence
2009-06-18, M3, Entreplan, KTH, Brinellvägen 64, Stockholm, 10:00 (English)
Opponent
Supervisors
Note
QC 20100714Available from: 2009-06-09 Created: 2009-06-09 Last updated: 2011-08-30Bibliographically approved

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