Adaptive Modelling of Two-Dimensional Shallow Water Flows
with Wetting and Drying ......................................... 1
Andreas Dedner, Dietmar Kröner, Nina Shokina
1 Introduction ................................................. 1
2 Runge-Kutta Discontinuous Galerkin Method for Shallow
Water Equations .............................................. 2
3 Well-Balancing ............................................... 5
4 Wetting and Drying Treatment ................................. 6
5 Implementation Notes ......................................... 8
6 Validation of Code ........................................... 8
6.1 "Lake at Rest" .......................................... 8
6.2 Dam Break Problem ....................................... 9
6.3 Drying Riemann Problem .................................. 9
6.4 Parabolic Bowl Problem ................................. 10
7 "Source-Sink" Problem - First Step towards Coupled
Modelling of Surface and Groundwater Flows .................. 11
References .................................................. 14
HPC Processor Technologies and Their Impact on Simulation ...... 17
Michael M. Resch, Uwe Küster
1 Introduction ................................................ 17
2 Hardware Challenges ......................................... 18
2.1 Building Blocks ........................................ 18
2.2 System Architectures ................................... 23
2.3 Operational Issues ..................................... 24
3 Software Challenges ......................................... 24
3.1 The Speed Issue ........................................ 24
3.2 The Scalability Issue .................................. 25
4 Solution Approaches ......................................... 25
5 Findings .................................................... 26
5.1 Science and Industry Gap ............................... 26
5.2 Wag the Tail? .......................................... 27
References .................................................. 27
A Parallel Implementation of FEM for a Boundary Value
Problem for the Shallow Water Equations ..................... 29
Evgeniya D. Karepova, Vladimir V. Shaidurov
1 Introduction ................................................ 29
2 The Modeling of Surface Waves by FEM ........................ 30
3 Parallel Algorithm .......................................... 33
4 Numerical Experiments ....................................... 37
5 Conclusion .................................................. 41
References .................................................. 41
Parallel FVTD for Solving Maxwell Equations in Dielectric-
Metal Composite Media .......................................... 43
Yurii I. Shokin, Lyudmila Yu. Prokopyeva, Mikhail
P. Fedoruk, Alexander S. Lebedev, Dmitry L. Chubarov
1 Introduction ................................................ 43
2 Finite Volume Time Domain Method ............................ 44
3 Parallel Implementation and Speedup Tests ................... 46
4 Numerical Results ........................................... 48
References .................................................. 49
Numerical Modeling of Work of Pulse Aerosol System of Fire
Fighting on Computer Clusters .................................. 51
Alexander D. Rychkov, Yurii I. Shokin
1 Introduction ................................................ 51
2 Description of Model and Governing Equations ................ 53
3 Parallel Algorithm .......................................... 57
4 Discussion of Results ....................................... 60
References .................................................. 63
Stagnant Vortex Flow ........................................... 65
Egon Krause
1 Introduction ................................................ 65
2 Stagnation Point in Inviscid Flow ........................... 68
3 Stagnant Viscous Flow ....................................... 71
4 Concluding Remarks .......................................... 73
References .................................................. 73
Numerical Modelling of Surface Water Waves Arising Due to
Movement of Underwater Landslide on Irregular Bottom Slope ..... 75
Leonid В. Chubarov, Gayaz S. Khakimzyanov, Nina Shokina
1 Introduction ................................................ 75
2 Problem Formulation ......................................... 76
3 Motion Law of Underwater Landslide .......................... 77
4 Model Area and Model Landslide .............................. 81
5 The Results of the Numerical Experiments .................... 82
5.1 Test Problem on Surface Wave Generation by Body
Movement on Horizontal Bottom .......................... 83
5.2 General Characteristics of Wave Regimes, Generated by
Landslide Movement on Irregular Slope .................. 85
5.3 Dependency on Landslide Dimensions ..................... 87
5.4 Dependency of Initial Depth of Landslide and Bottom
Slope .................................................. 89
6 Conclusion .................................................. 90
References .................................................. 91
Simulation of Geophysical Problems with Dune-Fem ............... 93
Slavko Brdar, Andreas Dedner, Robert Klöfkorn, Mirko
Kränkel, Dietmar Kröner
1 Introduction ................................................ 93
2 The Dune Interface Library - Recent Development ............. 94
3 Two-Phase Flow in Porous Media .............................. 94
3.1 Two-Phase Flow Problem ................................. 95
3.2 Numerical Results for the Two-Phase Flow Problem ....... 97
4 The Stokes-Darcy Problem .................................... 98
4.1 The Flow Equations ..................................... 98
4.2 The Beaver-Joseph Interface Condition .................. 99
4.3 Discretization ........................................ 100
4.4 Numerical Results ..................................... 100
5 Atmospheric Simulations .................................... 101
5.1 The Euler Equations with Moisture ..................... 101
5.2 Discretization ........................................ 103
5.3 Numerical Results ..................................... 104
References ................................................. 105
On Modeling of Mechanical Properties of Fibrous Composites .... 107
Kseniya S. Golushko, Sergey K. Golushko, Andrey V.
Yurchenko
1 Introduction ............................................... 107
2 Structural Models of Composite Materials ................... 108
3 Influence of CM-Models Selection on Simulation Results
for Rubber-Based Toroidal Shell ............................ 112
4 Influence of CM-Models Selection on Simulation Results
for Combined Pressure Vessels .............................. 115
References ................................................. 119
Well-Balanced Path-Consistent Finite Volume EG Schemes for
the Two-Layer Shallow Water Equations ......................... 121
Michael Dudzinski, Mária Lukáčová-Medvid'ová
1 Mathematical Model ......................................... 121
2 Operator Splitting Technique ............................... 123
3 Path-Consistent FVEG Scheme ................................ 126
4 Approximate Evolution Operators ............................ 127
5 Well-Balancing of Path-Consistent FVEG Scheme .............. 128
6 Numerical Experiments ...................................... 129
References ................................................. 135
Some Features of the Landslide Mechanism of Surface Waves
Generation in Real Basins ..................................... 137
Sofia A. Beisel, Leonid В. Chubarov, Yurii I. Shokin
1 Introduction ............................................... 137
2 Set-Up of Problem .......................................... 139
2.1 Model Reliefs ......................................... 139
2.2 Model Landslide ....................................... 140
3 Computational Results ...................................... 140
3.1 Dependence on Friction Angle .......................... 140
3.2 Dependence on Landslide Size .......................... 142
3.3 Dependence on Landslide Embedding ..................... 144
3.4 Dependence on Landslide Density ....................... 145
4 Conclusions ................................................ 146
References ................................................. 147
Multiscale Analyses for the Shallow Water Equations ........... 149
Didier Bresch, Rupert Klein, Carine Lucas
1 Introduction ............................................... 150
1.1 Governing Equations and Non-dimensionalization ........ 150
1.2 Asymptotic Flow Regimes and Organization of Paper ..... 151
2 Single-Scale Limit: "Lake Equations" ....................... 152
3 Inviscid Balanced Flow over Short-Wave Topography .......... 153
3.1 Weakly Nonlinear Regime ............................... 154
3.2 Fully Nonlinear Regime ................................ 157
4 Gravity Waves over Long-Wave Modulated Topography .......... 160
5 Conclusions ................................................ 162
References ................................................. 163
Shallow Water Equations for Shear Flows ....................... 165
Alexander A. Chesnokov, Valery Yu. Liapidevskii
1 Introduction ............................................... 165
2 Derivation of Long-Wave Model .............................. 167
2.1 Vertical Shear Flows .................................. 169
2.2 Horizontal Shear Flows ................................ 170
3 Generalized Hyperbolicity of Equations of Shear Flows ...... 171
3.1 Validation of Hyperbolicity Conditions ................ 172
4 Mixing Layer at Free Surface ............................... 174
4.1 Mean Flow Evolution ................................... 174
4.2 Velocity Field in Mixing Layer ........................ 176
5 Conclusions ................................................ 178
References ................................................. 178
A Language for the Definition of Fortran Source to Source
Transformations ............................................... 181
Uwe Küster
1 Compiler ................................................... 181
2 Self Defined Transformations ............................... 182
3 Transformation Language .................................... 183
3.1 Transformation Variables .............................. 183
3.2 Transformation Constructs ............................. 184
3.3 Self Defined Procedures in Transformation Code ........ 185
3.4 Intrinsic Procedures .................................. 185
3.5 Parsing Primitives in Parsing Mode .................... 186
4 Examples ................................................... 187
4.1 Unrolling of Source Code .............................. 187
4.2 Parsing Directive ..................................... 188
4.3 Insertion of Timing Calls ............................. 189
5 Concluding Remarks ......................................... 190
References ................................................. 190
Tsunami Modelling with Unstructured Grids. Interaction
between Tides and Tsunami Waves ............................... 191
Alexey Androsov, Jörn Behrens, Sergey Danilov
1 Introduction ............................................... 192
2 Barotropic Shallow Water Model ............................. 193
2.1 Boundary-Value Problem in Cartesian Coordinates ....... 193
2.2 Non-conforming Mixed P^c — P\ Discretization .......... 194
2.3 Momentum Advection Schemes ............................ 194
2.4 Other Implementation Details .......................... 197
3 Verification and Validation ................................ 198
3.1 Momentum Advection Test ............................... 198
3.2 Wetting and Drying .................................... 199
3.3 The Okushiri Test Case ................................ 199
3.4 Tsunami Simulation .................................... 201
4 Tide-Tsunami Interactions .................................. 202
5 Conclusion ................................................. 205
References ................................................. 206
A Geometry Independent Slope Limiter for the Discontinuous
Galerkin Method ............................................... 207
Vadym Aizinger
1 Introduction ............................................... 207
2 Mathematical Formulation ................................... 208
3 General Issues and Solution Strategy ....................... 209
4 Space Discretization, LDG Method ........................... 210
5 Slope Limiter .............................................. 212
6 Numerical Results .......................................... 214
6.1 Supercritical Flow in Constricted Channel ............. 214
6.2 Desalinization Plant in Galveston Bay ................. 215
7 Conclusions ................................................ 217
References ................................................. 217
Two-Fluid Barotropic Models for Powder-Snow Avalanche Flows ... 219
Yannick Meyapin, Denys Dutykh, Marguerite Gisclon
1 Introduction ............................................... 219
2 Two-Phase Flow Modelling ................................... 220
3 Velocity Relaxation ........................................ 222
4 Incompressible Limit ....................................... 228
5 Conclusions and Perspectives ............................... 230
References ................................................. 231
Hierarchy Analysis and Reduction of Reacting Flow Systems ..... 233
Viatcheslav Bykov, Ulrich Maas
1 Introduction ............................................... 233
1.1 Multi-scale Hierarchy and Manifolds Method ............ 234
1.2 Dynamics of Reacting Flows ............................ 236
2 Analysis of Chemical Kinetic Mechanisms .................... 238
2.1 SPS as Mathematical Model of Multi-scales Behaviour ... 238
2.2 ILDM Method - Local Analysis .......................... 240
2.3 Coordinate Free Singular Perturbations ................ 242
2.4 Linearly Decomposed Vector Fields, Problems of
Implementation ........................................ 242
2.5 Scale Invariant Form .................................. 243
2.6 Computational Tool of Manifold Analysis and
Reduction - Tabulation ................................ 244
3 Improvement and Coupling with Diffusion - REDIM ............ 246
3.1 Invariant Manifolds Concept ........................... 246
3.2 REDIM Method and Implementation Scheme ................ 247
4 Conclusions ................................................ 250
References ................................................. 251
Two-Dimensional Nonstationary Mathematical Model of Water
Catchment ..................................................... 253
Dmitry A. Burakov, Evgeniya D. Karepova, Vladimir
V. Shaidurov
1 Introduction ............................................... 253
2 Construction of Mathematical Model ......................... 254
2.1 Original Formulation of Problem ....................... 254
2.2 Depth Averaging ....................................... 256
2.3 Viscosity and Resistance Forces ....................... 258
3 Mathematical Model of Water Catchment ...................... 259
4 Energy Balance in Basin Model .............................. 263
5 Iterative Solution of Problem .............................. 264
6 Conclusion ................................................. 266
References ................................................. 266
Central-Upwind Schemes for Boussinesq Paradigm Equations ...... 267
Alina Chertock, Christo I. Christov, Alexander Kurganov
1 Introduction ............................................... 267
2 Boussinesq Paradigm Equation ............................... 268
3 Scheme and Algorithm for 1-D BPE ........................... 270
3.1 Description of 1-D Numerical Method ................... 271
3.2 1-D Numerical Experiments ............................. 273
4 2-D Numerical Experiments with BPE ......................... 276
4.1 Setting for 2-D Numerical Method ...................... 276
4.2 2-D Numerical Experiments ............................. 277
5 Conclusion ................................................. 280
References ................................................. 281
Parallel Lattice-Boltzmann Simulation of Transitional Flow
on Non-uniform Grids .......................................... 283
Maik Stiebler, Soren Freudiger, Manfred Krafczyk, Martin
Geier
1 Introduction ............................................... 283
2 Lattice Boltzmann Method with Subgrid Stress
Model (LBM-SGS) ............................................ 284
3 LBM-SGS on Irregular Grids ................................. 287
4 Test Case and Results ...................................... 288
4.1 Detailed Look at Case of Re = 10.000 .................. 290
5 Conclusion ................................................. 292
References ................................................. 293
Combined Approach to Numerical Simulation of Spatial
Nonlinear Waves in Shallow Water with Various Bottom
Topography .................................................... 297
Dmitry G. Arkhipov, Georgy A. Khabakhpashev, Nurziya
S. Safarova
1 Introduction ............................................... 297
2 Problem Formulation and Initial Equations .................. 298
3 Derivation of Model Equations .............................. 299
4 Discussion of the Numerical Results ........................ 302
5 Conclusion ................................................. 311
References ................................................. 311
Algorithm for Solving Non-stationary Three-Dimensional
Navier-Stokes Equations with Large Reynolds Numbers on
Multiprocessor Systems ........................................ 313
Nargozy T. Danaev, Dauren B. Zhakebaev, Abugamil U.
Abdibekov
1 Introduction ............................................... 313
2 Basic Equations ............................................ 314
3 Algorithm Solutions and Parallelization Algorithm .......... 315
4 Computing Experiment and Analysis of Results ............... 323
5 Conclusion ................................................. 325
References ................................................. 326
Numerical Modeling of Non-homogeneous Turbulence on Cluster
Computing System .............................................. 327
Ualikhan S. Abdibekov, Dauren B. Zhakebaev, Bakytzhan
T. Zhumagulov
1 Introduction ............................................... 327
2 Basic Equations, Problem ................................... 328
3 Numerical Method ........................................... 331
4 Defining Characteristics of Turbulence ..................... 331
5 Algorithms to Realize Initial and Boundary Conditions ...... 333
6 Simulation Results ......................................... 333
7 Conclusion ................................................. 338
References ................................................. 338
Dynamic Finite Element Analysis of Cancellous Bone Micro
Structure ..................................................... 339
Ralf Schneider, Ulrich Hindenlang, Peter Copf
1 Introduction ............................................... 339
2 Material and Methods ....................................... 340
2.1 Bone Specimen - Geometry Reconstruction ............... 340
2.2 Model Configurations .................................. 341
3 Results .................................................... 343
3.1 Dynamic Analysis of Single Trabecula .................. 343
3.2 Static Simulation ..................................... 344
3.3 Dynamic Analysis of Cancellous Bone Sample ............ 345
4 Conclusion ................................................. 346
References ................................................. 347
Three-Dimensional Numerical Modeling of Stratified Flows in
Littoral Zone of Israel Using Shallow Water Approximation ..... 349
Michael Sladkevich, Anna Levin, Eliezer Kit
1 Introduction ............................................... 349
2 Model Description .......................................... 350
3 Model Calibration .......................................... 354
4 Model Verification ......................................... 355
5 Model Limitation ........................................... 359
6 Conclusions ................................................ 360
References ................................................. 361
A Cartesian Cut-Cell Solver for Compressible Flows ............ 363
Daniel Hartmann, Matthias Meinke, Wolfgang Schröder
1 Introduction ............................................... 363
2 Governing Equations ........................................ 364
3 Numerical Method ........................................... 365
3.1 Evaluation of Surface Fluxes .......................... 366
3.2 Representation of Embedded Boundaries ................. 368
4 Results .................................................... 370
4.1 Flow Past Sphere ...................................... 371
5 Conclusions ................................................ 375
References ................................................. 376
Author Index .................................................. 377
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