Computational Science and High Performance Computing IV (eBook)

Egon Krause retired in 1998 from the chair of fluid mechanics at the RWTH Aachen.Yuri Shokin is a full member of the Russian Academy of Sciences, the director of the Institute of Computational Technologies of the Siberian Branch of the Russian Academy of Sciences (ICT SB RAS), the director of the Technopark Novosibirsk and a full professor of the Novosibirsk State University.Dietmar Kröner is the full professor at the Section of Applied Mathematics of the University of Freiburg (IAM Freiburg).Michael Resch is the director of the High Performance Computing Center Stuttgart (HLRS) and a full professor for Supercomputing at the University of Stuttgart.Nina Shokina is a researcher at the the Section of Applied Mathematics of the University of Freiburg (IAM Freiburg) and a researcher at the Institute of Computational Technologies of the Siberian Branch of the Russian Academy of Sciences (ICT SB RAS).Dietmar Kröner is the full professor at the Section of Applied Mathematics of the University of Freiburg (IAM Freiburg).Nina Shokina is a researcher at the the Section of Applied Mathematics of the University of Freiburg (IAM Freiburg) and a researcher at the Institute of Computational Technologies of the Siberian Branch of the Russian Academy of Sciences (ICT SB RAS).

Title 1
Preface 5
Contents 7
Adaptive Modelling of Two-Dimensional Shallow Water Flows with Wetting and Drying 21
Introduction 21
Runge-Kutta Discontinuous Galerkin Method for Shallow Water Equations 22
Well-Balancing 25
Wetting and Drying Treatment 26
Implementation Notes 28
Validation of Code 28
"Lake at Rest" 28
Dam Break Problem 29
Drying Riemann Problem 29
Parabolic Bowl Problem 30
“Source-Sink” Problem - First Step towards Coupled Modelling of Surface and Groundwater Flows 31
References 34
HPC Processor Technologies and Their Impact on Simulation 36
Introduction 36
Hardware Challenges 37
Building Blocks 37
System Architectures 42
Operational Issues 43
Software Challenges 43
The Speed Issue 43
The Scalability Issue 44
Solution Approaches 44
Findings 45
Science and Industry Gap 45
Wag the Tail? 46
References 46
A Parallel Implementation of FEM for a Boundary Value Problem for the Shallow Water Equations 48
Introduction 48
The Modeling of Surface Waves by FEM 49
Parallel Algorithm 52
Numerical Experiments 56
Conclusion 60
References 60
Parallel FVTD for Solving Maxwell Equations in Dielectric-Metal Composite Media 62
Introduction 62
Finite Volume Time Domain Method 63
Parallel Implementation and Speedup Tests 65
Numerical Results 67
Numerical Modeling of Work of Pulse Aerosol System of Fire Fighting on Computer Clusters 69
Introduction 69
Description of Model and Governing Equations 71
Parallel Algorithm 75
Discussion of Results 78
References 81
Stagnant Vortex Flow 82
Introduction 82
Stagnation Point in Inviscid Flow 85
Stagnant Viscous Flow 88
Concluding Remarks 90
References 90
Numerical Modelling of SurfaceWater Waves Arising Due to Movement of Underwater Landslide on Irregular Bottom Slope 92
Introduction 92
Problem Formulation 93
Motion Law of Underwater Landslide 94
Model Area and Model Landslide 98
The Results of the Numerical Experiments 99
Test Problem on Surface Wave Generation by Body Movement on Horizontal Bottom 100
General Characteristics of Wave Regimes, Generated by Landslide Movement on Irregular Slope 102
Dependency on Landslide Dimensions 104
Dependency of Initial Depth of Landslide and Bottom Slope 106
Conclusion 107
References 108
Simulation of Geophysical Problems with DUNE-FEM 109
Introduction 109
TheDUNE Interface Library – Recent Development 110
Two-Phase Flow in Porous Media 110
Two-Phase Flow Problem 111
Numerical Results for the Two-Phase Flow Problem 113
The Stokes-Darcy Problem 114
The Flow Equations 114
The Beaver-Joseph Interface Condition 115
Discretization 116
Numerical Results 116
Atmospheric Simulations 117
The Euler Equations with Moisture 117
Discretization 119
Numerical Results 120
References 121
On Modeling of Mechanical Properties of Fibrous Composites 123
Introduction 123
Structural Models of Composite Materials 124
Influence of CM-Models Selection on Simulation Results for Rubber-Based Toroidal Shell 128
Influence of CM-Models Selection on Simulation Results for Combined Pressure Vessels 131
References 135
Well-Balanced Path-Consistent Finite Volume EG Schemes for the Two-Layer Shallow Water Equations 137
Mathematical Model 137
Operator Splitting Technique 139
Path-Consistent FVEG Scheme 142
Approximate Evolution Operators 143
Well-Balancing of Path-Consistent FVEG Scheme 144
Numerical Experiments 145
References 151
Some Features of the Landslide Mechanism of Surface Waves Generation in Real Basins 152
Introduction 152
Set-Up of Problem 154
Model Reliefs 154
Model Landslide 155
Computational Results 155
Dependence on Friction Angle 155
Dependence on Landslide Size 157
Dependence on Landslide Embedding 159
Dependence on Landslide Density 160
Conclusions 161
References 162
Multiscale Analyses for the Shallow Water Equations 164
Introduction 165
Governing Equations and Non-dimensionalization 165
Asymptotic Flow Regimes and Organization of Paper 166
Single-Scale Limit: “Lake Equations” 167
Inviscid Balanced Flow over Short-Wave Topography 168
Weakly Nonlinear Regime 169
Fully Nonlinear Regime 172
GravityWaves over Long-Wave Modulated Topography 175
Conclusions 177
References 178
ShallowWater Equations for Shear Flows 180
Introduction 180
Derivation of Long-Wave Model 182
Vertical Shear Flows 184
Horizontal Shear Flows 185
Generalized Hyperbolicity of Equations of Shear Flows 186
Validation of Hyperbolicity Conditions 187
Mixing Layer at Free Surface 189
Mean Flow Evolution 189
Velocity Field in Mixing Layer 191
Conclusions 193
References 193
A Language for the Definition of Fortran Source to Source Transformations 195
Compiler 195
Self Defined Transformations 196
Transformation Language 197
Transformation Variables 197
Transformation Constructs 198
Self Defined Procedures in Transformation Code 199
Intrinsic Procedures 199
Parsing Primitives in Parsing Mode 200
Examples 201
Unrolling of Source Code 201
Parsing Directive 202
Insertion of Timing Calls 203
Concluding Remarks 204
References 204
Tsunami Modelling with Unstructured Grids. Interaction between Tides and Tsunami Waves 205
Introduction 206
Barotropic Shallow Water Model 207
Boundary-Value Problem in Cartesian Coordinates 207
Non-conforming Mixed $PNC1 P1$ Discretization 208
Momentum Advection Schemes 208
Other Implementation Details 211
Verification and Validation 212
Momentum Advection Test 212
Wetting and Drying 213
The Okushiri Test Case 213
Tsunami Simulation 215
Tide-Tsunami Interactions 216
Conclusion 219
References 220
A Geometry Independent Slope Limiter for the Discontinuous Galerkin Method 221
Introduction 221
Mathematical Formulation 222
General Issues and Solution Strategy 223
Space Discretization, LDG Method 224
SlopeLimiter 226
Numerical Results 228
Supercritical Flow in Constricted Channel 228
Desalinization Plant in Galveston Bay 229
Conclusions 231
References 231
Two-Fluid Barotropic Models for Powder-Snow 3Avalanche Flows 232
Introduction 232
Two-Phase Flow Modelling 233
Velocity Relaxation 235
Incompressible Limit 241
Conclusions and Perspectives 243
References 244
Hierarchy Analysis and Reduction of Reacting Flow Systems 246
Introduction 246
Multi-scale Hierarchy and Manifolds Method 247
Dynamics of Reacting Flows 249
Analysis of Chemical Kinetic Mechanisms 251
SPS as Mathematical Model of Multi-scales Behaviour 251
ILDM Method - Local Analysis 253
Coordinate Free Singular Perturbations 255
Linearly Decomposed Vector Fields, Problems of Implementation 255
Scale Invariant Form 256
Computational Tool of Manifold Analysis and Reduction - Tabulation 257
Improvement and Coupling with Diffusion - REDIM 259
Invariant Manifolds Concept 259
REDIM Method and Implementation Scheme 260
Conclusions 263
References 264
Two-Dimensional Nonstationary Mathematical Model of Water Catchment 266
Introduction 266
Construction of Mathematical Model 267
Original Formulation of Problem 267
Depth Averaging 269
Viscosity and Resistance Forces 271
Mathematical Model ofWater Catchment 272
Energy Balance in Basin Model 276
Iterative Solution of Problem 277
Conclusion 279
References 279
Central-Upwind Schemes for Boussinesq Paradigm Equations 280
Introduction 280
Boussinesq Paradigm Equation 281
Scheme and Algorithm for 1-D BPE 283
Description of 1-D Numerical Method 284
1-D Numerical Experiments 286
2-D Numerical Experiments with BPE 289
Setting for 2-D Numerical Method 289
2-D Numerical Experiments 290
Conclusion 293
References 294
Parallel Lattice-Boltzmann Simulation of Transitional Flow on Non-uniform Grids 295
Introduction 295
Lattice Boltzmann Method with Subgrid Stress Model (LBM-SGS) 296
LBM-SGS on Irregular Grids 299
Test Caseand Results 300
Detailed Look at Case of Re = 10.000 302
Conclusion 304
References 305
Combined Approach to Numerical Simulation of Spatial NonlinearWaves in Shallow Water with Various Bottom Topography 308
Introduction 308
Problem Formulation and Initial Equations 309
Derivation of Model Equations 310
Discussion of the Numerical Results 313
Conclusion 322
References 322
Algorithm for Solving Non-stationary Three-Dimensional Navier-Stokes Equations with Large Reynolds Numbers on Multiprocessor Systems 324
Introduction 324
Basic Equations 325
Algorithm Solutions and Parallelization Algorithm 326
Computing Experiment and Analysis of Results 334
Conclusion 336
References 337
Numerical Modeling of Non-homogeneous Turbulence on Cluster Computing System 338
Introduction 338
Basic Equations, Problem 339
Numerical Method 342
Defining Characteristics of Turbulence 342
Algorithms to Realize Initial and Boundary Conditions 344
Simulation Results 344
Conclusion 349
References 349
Dynamic Finite Element Analysis of Cancellous Bone Micro Structure 350
Introduction 350
Material and Methods 351
Bone Specimen - Geometry Reconstruction 351
Model Configurations 352
Results 354
Dynamic Analysis of Single Trabecula 354
Static Simulation 355
Dynamic Analysis of Cancellous Bone Sample 356
Conclusion 357
References 358
Three-Dimensional Numerical Modeling of Stratified Flows in Littoral Zone of Israel Using Shallow Water Approximation 359
Introduction 359
Model Description 360
Model Calibration 364
Model Verification 365
Model Limitation 369
Conclusions 370
References 371
A Cartesian Cut-Cell Solver for Compressible Flows 372
Introduction 372
Governing Equations 373
Numerical Method 374
Evaluation of Surface Fluxes 375
Representation of Embedded Boundaries 377
Results 379
Flow Past Sphere 380
Conclusions 384
References 385
Author Index 386