Efficient Numerical Methods and Information-Processing Techniques for Modeling Hydro- and Environmental Systems

319 Pages·2005·14.93 MB·English

by  Professor Dr. Reinhard Hinkelmann (auth.)

Lecture Notes in Applied
and Computational Mechanics
Volume 21
Series Editors
Prof. Dr.-Ing. Friedrich Pfeiffer
Prof. Dr.-Ing. Peter Wriggers
Efficient Numerical Methods
and Information- Processing
Techniques for Modeling
Hydro- and Environmental
Systems
Reinhard Hinkelmann
-
Springer
Professor Dr. REINHARDH INKELMANN
Technische Universitat Berlin
Institut fiir Bauingenieurwesen
Fachgebiet Wasserwirtschaft und Hydroinformatik
StraRe des 17. Juni 144
10623 Berlin, Germany
With 179 Figures
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Preface
In recent years, numerical simulation models have become indispensable in
hydro-andenvironmentalsciencesandengineering,mainlyformakingpredic-
tions and improving process understanding. For many problems, a physically
correct and mathematically accurate simulation of the coupled complex pro-
cessesrequirespowerfulnumericalmethodsaswellashighresolutionsinspace
and time. In information processing, many techniques have been developed
for setting up systems with complex geometries and parameter distributions,
and high-performance computer systems are available for fast computations.
Overall, there is an urgent need for the further development and application
of efficient numerical simulation models in environment water which consist
ofefficientnumericalmethodsassociatedwithefficientinformation-processing
techniques.
After a general introduction to numerical simulation in environment water,
the basic equations for groundwater flow and transport processes, for mul-
tiphase / multicomponent flow and transport processes in the subsurface as
well as for flow and transport processes in surface waters are briefly deduced
from the general form of the balance equation. The state of the art of dis-
cretization and stabilization methods (e.g. Finite-Difference, Finite-Element
and Finite-Volume Methods), parallel methods and adaptive methods as well
asfastsolvers(e.g.ConjugateGradient,MultigridMethods)ispresentedwith
particular focus on explaining the interactions of the different methods. Par-
allel, adaptive and Conjugate Gradient or Multigrid Methods can collabo-
rate well and should be chosen to solve large-scale problems. An overview
of various information-processing techniques, which must work efficiently to-
gether is provided, briefly dealing with preprocessing (e.g. Computer Aided
Design, databases, mesh generation, geostatistical methods), processing (e.g.
High-Performance Computing, modeling system MUFTE-UG) and postpro-
cessing tools(e.g.advancedvisualization)as wellas Internet-based Collabora-
tive Engineering. Eventually, the interactions of the numerical methods with
the information-processing techniques in order to achieve efficient numerical
VI Preface
simulationsaredemonstratedfor awide rangeofapplicationsin environment
water. The work includes contributions to an improvement of process un-
derstanding, to further developments of numerical methods and information-
processing,aswellastonewapplicationfieldsforexisting simulationmodels.
Finally, future perspectives are pointed out.
This book summarizes about a decade of my work in the field of numerical
simulation of flow and transport processes in hydro- and environmental sci-
encesandengineeringcarriedoutatthreedifferentinstitutesinGermany,the
Institute for Fluid Mechanics and Computer Applications in Civil Engineer-
ing, University of Hannover,the Institute for Computer Applications in Civil
Engineering, Technical University of Braunschweig, and the Department of
Hydromechanics and Modeling of Hydrosystems, Institute of Hydraulic Engi-
neering, University of Stuttgart. This book is based on the similarly entitled
habilitation which I made at the Faculty of Civil and Environmental Engi-
neeringattheUniverstiyofStuttgart.Asthingschangewithtime,Iswitched
to the Department of Water Resources Management and Hydroinformatics,
Institute of Civil Engineering, Technical University of Berlin.
Iwouldliketothankmostspeciallymyformer’boss’andfriend,Prof.Rainer
Helmig, for numerous fruitful discussions, permanent support and great free-
dom in carrying out my work.
Thediscussionswiththecolleaguesofthethreeaforementionedinstitutescon-
tributedagreatdealtothe progressofthiswork.Theirhelpfulness,qualifica-
tions and collaborationas well as the longstanding goodworking atmosphere
will always remain in my mind. I specially want to thank several colleagues
from Braunschweig and Stuttgart for their excellent help and support: An-
dreas Bielinski, Thomas Breiting, Dr. Holger Class, Dr. Ken Kobayashi, Dr.
Lina Neunha¨userer, Steffen Ochs, Ulrich O¨lmann, Dr. Maren Paul, Dr. Hus-
sam Sheta and Bjo¨rn Witte. Many, many thanks to Prudence Lawday for
correcting my English drafts and to Brigitte von der Ohe for designing many
figures, improving the layout etc.
Finally, I very specially thank my partner Christine Barlag and my children
Timon and Schirin Barlag for their understanding and support, and I apolo-
gize my frequent absence from home in the last years.
Berlin, Hannover
September 2004 Reinhard ’Phillip’ Hinkelmann
Contents
Preface .................................................... V
Contents...................................................VII
Nomenclature ............................................. XI
1 Introduction............................................... 1
1.1 Systems and scales ...................................... 1
1.2 Numerical process simulation ............................. 6
1.3 Model concepts and modeling systems...................... 8
1.3.1 Model concepts ................................... 8
1.3.2 Modeling systems ................................. 11
1.3.3 Need for laboratory and field experiments ............ 13
1.4 Deficits and objectives of the work......................... 15
1.4.1 Deficits .......................................... 15
1.4.2 Objectives of the work ............................. 16
2 Physical and mathematical model concepts ................ 19
2.1 Physical model concepts.................................. 19
2.1.1 Continuum-mechanical consideration................. 19
2.1.2 Subsurface systems ................................ 20
2.1.3 Surface-water systems.............................. 24
2.2 General form of the balance equation ...................... 27
2.3 Mathematical model concept for groundwater flow and
transport processes ...................................... 29
2.3.1 Flow processes .................................... 29
2.3.2 Transport processes................................ 32
2.4 Mathematical model concept for two-phase flow processes in
the subsurface .......................................... 37
2.4.1 Continuity equation ............................... 37
2.4.2 Momentum equation............................... 38
VIII Contents
2.4.3 Constitutive relations .............................. 39
2.4.4 Two-phase flow equations .......................... 42
2.5 Mathematicalmodelconceptfortwo-phase/multicomponent
flow and transport processes in the subsurface............... 44
2.5.1 Continuity and momentum equation ................. 45
2.5.2 Constitutive relationships .......................... 45
2.5.3 Two-phase / three-component flow and transport
equations......................................... 46
2.6 Mathematicalmodel conceptfor flowandtransportprocesses
in surface water ......................................... 48
2.6.1 Flow processes .................................... 48
2.6.2 Transport processes................................ 53
3 Efficient numerical methods ............................... 55
3.1 Discretization and stabilization methods.................... 55
3.1.1 General requirements .............................. 55
3.1.2 Time discretization ................................ 58
3.1.3 Finite-Difference Methods .......................... 62
3.1.4 Finite-Element Methods............................ 72
3.1.5 Finite-Volume Methods ............................ 84
3.1.6 Some other methods ............................... 94
3.2 Parallelmethods ........................................ 97
3.2.1 Development of High-Performance Computing ........ 98
3.2.2 Parallelizationstrategies ........................... 98
3.2.3 Parallelizationof basic tasks ........................100
3.2.4 Load balancing....................................107
3.2.5 Particle Methods and series.........................112
3.2.6 Recommendations .................................114
3.2.7 Examples ........................................114
3.3 Adaptive methods .......................................118
3.3.1 Different methods and techniques of adaptation .......118
3.3.2 Error estimators and indicators .....................123
3.3.3 Refinement and coarsening .........................130
3.3.4 Examples ........................................135
3.4 Fast solvers.............................................139
3.4.1 Introduction ......................................139
3.4.2 Single-grid solvers .................................140
3.4.3 Preconditioners ...................................147
3.4.4 Multigrid solvers ..................................151
3.4.5 Non-linear solvers .................................160
3.4.6 Examples ........................................162
Contents IX
4 Efficient information-processing techniques ................167
4.1 Preprocessing ...........................................167
4.1.1 Introduction ......................................167
4.1.2 CAD systems .....................................170
4.1.3 Database-managementsystems......................172
4.1.4 Tomography and scanning..........................173
4.1.5 Geographical Information Systems...................175
4.1.6 Geostatistical methods .............................178
4.1.7 Mesh generation ..................................180
4.2 Processing..............................................184
4.2.1 High-Performance Computational Architectures .......184
4.2.2 Networks and communication in HPC................187
4.2.3 Performance numbers ..............................189
4.2.4 MUFTE-UG......................................191
4.3 Postprocessing ..........................................196
4.4 WWW-based Collaborative Engineering....................199
4.4.1 Introduction ......................................199
4.4.2 Software tools and hardware requirements ............200
4.4.3 HydroWeb........................................202
5 Applications ...............................................205
5.1 Groundwater flow and transport processes ..................205
5.1.1 Motivation of the equidimensional modeling approach
for fracture-matrix systems .........................206
5.1.2 The numerical algorithm ...........................208
5.1.3 Extension of the mesh generator ART................208
5.1.4 Comparisonof the low- and equidimensional modeling
approaches .......................................209
5.1.5 Comparison of upwind methods .....................212
5.1.6 Adaptive methods .................................212
5.1.7 Evaluation and future work.........................217
5.2 Two-phase flow processes in the subsurface .................218
5.2.1 Numerical algorithm...............................218
5.2.2 Example: Methane migration processes in coal mining
areas ............................................219
5.2.3 Example: Gas-water flow processes in dike systems ....232
5.2.4 Example: Multi-step outflow experiment..............236
5.3 Two-phase / multicomponent processes in the subsurface .....238
5.3.1 Numerical algorithm...............................238
5.3.2 Example: Two-phase / multicomponent flow
and transport processes in the interaction area
groundwater - surface water ........................238
5.4 Flow and transport processes in surface water...............248
5.4.1 Vertically-integrated flow and transport processes in
shallow water .....................................248
X Contents
5.4.2 Three-dimensional flow and transport processes in
shallow water .....................................263
6 Summary and conclusions .................................277
References.....................................................283
Index..........................................................301
Nomenclature
terms with Latin letters
symbol dimension definition
b [m] constant aperture
c [m] correlation length
c [mg/l] tracer concentration
c [m/s] wave velocity
c unknown variable
cˆ nodal value
c˜ [mg/l] approximated concentration
c [−] wind-stress coefficient
D
d [m] characteristic length on the microscale
e error
e [−] scalar entity
e [%] parallel efficiency
p
f [−] damping function
f quantities water level h
g [−] damping function
g [m/s2] gravity
g exact solution of the partial differential equation
g numerical solution of the discretized equation
g [m/s2] gravity vector (0,0,−g)T
gx exact solution of the discretized equation
h [m] piezometric head
h [m] water level
h˜ [m] approximated piezometric head
k [−] relative permeability
rα
l [m] discretization length of element i
i
l [m] mixing length
m