Progress in Industrial Mathematics at ECMI 2004 (eBook)

Preface 5
Contents 7
Part I Theme: Aerospace 31
The MEGAFLOW Project – Numerical Flow Simulation for Aircraft 32
1 Introduction 32
2 MEGAFLOW software 33
3 Software validation 42
4 Industrial Applications 45
5 Multidisciplinary simulations 52
6 Numerical optimization 54
7 Conclusions and perspective 58
References 59
Gradient Computations for Optimal Design of Turbine Blades 63
1 Introduction 63
2 Model Problem 63
3 Gradient Computation 65
4 Optimal Turbine Blade 66
References 67
Fast Numerical Computing for a Family of Smooth Trajectories in Fluids Flow 68
1 Introduction 68
2 Fitting trajectories with cubic polynomials 69
3 Computing splines 70
4 Valuating splines 70
5 Computing values of splines 72
6 Conclusions 72
References 72
Optimal Control of an ISS-Based Robotic Manipulator with Path Constraints 73
1 Introduction 73
2 Optimal Control Problem 74
3 Transformation into Minimum Coordinates 74
4 Optimal Control Theory 76
5 Numerical Example 77
References 77
Rigorous Analysis of Extremely Large Spherical Reflector Antennas: EM Case 78
1 Introduction 78
2 The Decoupled System at High Frequencies 79
3 Algorithm Performance on the Decoupled System 81
4 Conclusions 82
References 82
Part II Theme: Electronic Industry 84
Simulation and Measurement of Interconnects and On- Chip Passives: Gauge Fields and Ghosts as Numerical Tools 86
1 Introduction 86
2 The Maxwell Equations and the Drift-Di.usion Equations 88
3 Gauge Fields and Ghost Fields 90
4 Applications 94
5 Conclusions 101
References 102
Eigenvalue Problems in Surface Acoustic Wave Filter Simulations 103
1 Introduction 104
2 Problem Description and First Model Assumptions 106
3 The Piezoelectric Equations 108
4 A Scalar Model Problem 110
5 Piezoelectric Equations and Periodic Structures 116
6 Numerical Results 122
7 Conclusions 125
References 126
Diffraction Grating Theory with RCWA or the C Method 128
1 Introduction 128
2 Mathematical problem 129
3 Solution methods 129
4 Results 131
References 132
Relocation of Electric Field Domains and Switching Scenarios in Superlattices 133
1 Introduction 133
2 The Sequential Tunnelling Model 134
3 Switching Scenarios 135
References 137
Quantum Kinetic and Drift-Diffusion Equations for Semiconductor Superlattices 138
References 142
Model Order Reduction of Nonlinear Dynamical Systems 143
1 Introduction 143
2 Linear time-varying systems 144
3 Nonlinear systems 145
4 Illustrative numerical example 146
References 147
Electrolyte Flow and Temperature Calculations in Finite Cylinder Caused by Alternating Current 148
1 Introduction 148
2 Mathematical Model 149
3 The Finite-Di.erence Approximations and Numerical Results. 150
4 Conclusion 151
References 152
Numerical Simulation of the Problem Arising in the Gyrotron Theory 153
1 Introduction 153
2 Numerical Simulation 155
3 Conclusions 157
References 157
A Deterministic Multicell Solution to the Coupled Boltzmann- Poisson System Simulating the Transients of a 2D- Silicon MESFET 158
1 Introduction 158
2 Physical Assumptions 159
3 The Multicell Method for Spatially Two-Dimensional Problems 160
4 Numerical Results 161
Some Remarks on the Vector Fitting Iteration 163
1 Introduction 163
2 An iterative scheme for solving rational LS problems 164
3 The Vector Fitting methodology 165
4 How VF .ts in 165
5 Initial pole placement 167
References 167
Krylov Subspace Methods in the Electronic Industry 168
1 Introduction 168
2 Equation setting 169
3 Model Order Reduction 169
4 Validation of results 171
5 Redundancy 171
6 Conclusions 172
References 172
On Nonlinear Iteration Methods for DC Analysis of Industrial Circuits 173
1 Introduction 173
2 Equation formulation 174
3 Line-search methods 175
4 Trust-region methods 175
5 Non-monotone strategy 175
6 Dog-leg method 175
7 Tensor methods 176
8 Results 176
References 177
Implementing Efficient Array Traversing for FDTD- lumped Element Cosimulation 178
1 Introduction 178
2 Implementing the Data Types and Array Traversing 179
3 Comparison of the Two Data Types 180
Thermal Modeling of Bottle Glass Pressing 183
1 Introduction 183
2 Physical model 183
3 Finite element model 185
4 Results 186
5 Conclusions 187
References 187
Simulation of Pulsed Signals in MPDAE- Modelled SC- Circuits 188
1 Introduction 188
2 Switched capacitor .lter 188
3 Multidimensional approach 189
4 Miller integrator 191
5 Conclusions 192
References 192
A More Efficient Rigorous Coupled-Wave Analysis Algorithm 193
1 Introduction 193
2 The model 194
3 The equations and boundary conditions 195
4 Numerical results 197
5 Conclusions 197
References 197
Iterative Solution Approaches for the Piezoelectric Forward Problem 198
1 Introduction 198
2 Mathematical Model 199
3 Iterative Solution 199
4 Numerical Experiments 200
Hydrodynamic Modeling of an Ultra-Thin Base Silicon Bipolar Transistor 203
1 Introduction 203
2 The Extended Hydrodynamic Model 204
3 Limit Models 204
4 Numerical Results 205
References 207
Warped MPDAE Models with Continuous Phase Conditions 208
1 Introduction 208
2 Multivariate Signal Model 209
3 Warped MPDAE System 210
4 Numerical Simulation 210
5 Conclusions 212
References 212
Exact Closure Relations for the Maximum Entropy Moment System in Semiconductor Using Kane’s Dispersion Relation 213
1 The Maximum Entropy Moment Systems for Electrons in Semiconductors 213
2 Solvability of the Maximum Entropy Problem 215
3 The Euler-Poisson Model 216
References 217
Reduced Order Models for Eigenvalue Problems 218
1 Introduction 218
2 Reduced Order Modelling Problem 219
3 Reduced Order Modelling Methods 219
4 New Research Directions 221
References 222
DRK Methods for Time-Domain Oscillator Simulation 223
1 Introduction 223
2 DRK methods 223
3 Two-stage Example 225
4 Alternative Formulation 226
5 Conclusions 227
References 227
Digital Linear Control Theory Applied To Automatic Stepsize Control In Electrical Circuit Simulation 228
1 Introduction to error control 228
2 Control-Theoretic Approach to Stepsize Control 229
3 Derivation of Process Model for BDF-Methods 230
4 Design of Finite Order Digital Linear Stepsize Controller 230
5 Numerical Experiments 231
6 Conclusions 232
References 232
Part III Theme: Chemical Technology 234
On the Dynamics of a Bunsen Flame 236
1 Introduction 236
2 Flame front dynamics 236
3 Solution in the case of a Poiseuille .ow 237
4 Flame response to .ow perturbations 239
References 240
Index Analysis for Singular PDE Models of Fuel Cells 241
1 Time Index: De.nition and Prototype Example 241
2 Time Index of Dynamic Fuel Cell Models 243
References 245
On the Modeling of the Phase Separation of a Gelling Polymeric Mixture 246
1 Introduction 246
2 Theory 247
4 Conclusion 249
References 250
Iso-Surface Analysis of a Turbulent Diffusion Flame 251
1 Introduction 251
2 Di.usion .ame in a mixing layer 252
3 Iso-surface analysis of turbulent .ame properties 253
References 255
A Simplified Model for Non–Isothermal Crystallization of Polymers 256
1 Introduction 256
2 Temperature Equation with Memory 257
3 Numerical Results 258
Numerical Simulation of Cylindrical Induction Heating Furnaces 261
1 Introduction 261
2 Mathematical modelling 262
3 Numerical solution 264
References 265
Thermal Radiation E.ect on Thermal Explosion in a Gas Containing Evaporating Fuel Droplets. 266
1 Introduction 266
2 Physical model 267
3 Conclusions 270
References 270
Local Defect Correction for Laminar Flame Simulation 271
1 Introduction 271
2 An outline of LDC 271
3 Constructing an orthogonal curvilinear grid 273
4 The thermo-di.usive model for laminar .ames 274
References 275
Development of a Hierarchical Model Family for Molten Carbonate Fuel Cells with Direct Internal Reforming ( DIR- MCFC) 276
Introduction 276
MCFC Working Principle 277
The Reference Model 278
Simulation Results and Model Applications 279
References 280
Modelling of Filtration and Regeneration Processes in Diesel Particulate Traps 281
1 Introduction 281
2 Simulation model 282
3 Results 284
4 Conclusion and Outlook 284
References 285
Modelling the Shelf Life of Packaged Olive Oil Stored at Various Conditions 286
1 Introduction 286
2 Experimental 287
3 Theory 287
4 Result and Discussion 288
5 Conclusion 290
References 290
Nonlinear Model Reduction of a Dynamic Two- dimensional Molten Carbonate Fuel Cell Model 291
1 Introduction 291
2 Spatially Distributed Reference Model of the MCFC 292
3 Derivation of the Reduced MCFC Model 292
4 Validation of the Reduced Model 294
5 Conclusions 295
References 295
Liquid/Solid Phase Change with Convection and Deformations: 2D Case 297
1 Introduction 297
2 Governing Equations and Reformulation 298
3 Numerical Test and Conclusions 299
Mathematical Modelling of Mass Transport Equations in Fixed- Bed Absorbers 302
1 Introduction 302
2 Dimensionless model 303
3 Application: Working Capacity test 306
4 Conclusions 306
References 306
Injection Vapour Model in a Porous Medium Accounting for a Weak Condensation 307
1 Motivating Problem and Mathematical Model 307
2 Comparisons with Experimental Data 310
References 311
Multigrid Solution of Three-Dimensional Radiative Heat Transfer in Glass Manufacturing 312
1 Introduction 312
2 Radiative Heat Transfer in Glass Manufacturing 313
3 Multigrid Solution Procedure 314
4 Results 315
References 316
DEM Simulations of the DI Toner Assembly 317
1 Introduction 317
2 Force Models 318
3 Results 320
4 Conclusion 320
References 321
Modeling of Drying Processes in Pore Networks 322
1 Introduction 322
2 Pore network modeling of drying without the presence of liquid . lms 323
3 The e.ect of liquid .lms 325
4 Conclusions 326
References 326
Mathematical Modelling of Flow through Pleated Cartridge Filters 327
Introduction 327
Mathematical Statement of the Combined Stokes/Darcy Flow Regimes 327
Results and Discussions 329
References 331
Comparison of Some Mixed Integer Non-linear Solution Approaches Applied to Process Plant Layout Problems 332
1 Introduction 332
2 Problem formulation 333
3 Non-Linear Solution Approaches 333
4 Illustrative examples 334
5 Conclusions 335
A Mathematical Model of Three-Dimensional Flow in a Scraped- Surface Heat Exchanger 337
1 Scraped-Surface Heat Exchangers (SSHEs) 337
2 Transverse Flow 338
3 Longitudinal Flow 340
4 Summary 341
Acknowledgements 341
References 341
Part IV Theme: Life Sciences 343
Transmission Line Matrix Modeling of Sound Wave Propagation in Stationary and Moving Media 344
1 Introduction 344
2 TLM Model of Stationary Media 345
3 TLM Model of Moving Media 347
4 Conclusion 347
References 348
Viscous Drops Spreading With Evaporation And Applications To DNA Biochips 349
1 Introduction 349
2 The physical model and the lubrication approximation 350
References 353
Similarity-Based Object Recognition of Airborne Fungi in Digital Images 354
1 Introduction 354
2 Fungi Images 354
3 Similarity-Based Object Recognition 355
4 Results 357
5 Conclusions 358
References 358
Rivalling Optimal Control in Robot- Assisted Surgery 359
1 Introduction 359
2 Manipulator Model 360
3 Optimal Control 360
4 Optimal Control Constraints 361
5 Example: Constrained Motion and Rivalling Control 363
References 363
Part V Theme: Materials 365
A Multiphase Model for Concrete: Numerical Solutions and Industrial Applications 366
Physical and mathematical model 366
1 Numerical solution 369
Application of the model to young concrete 369
Numerical simulation of self-desiccation process 371
2 Application of the model to concrete structures in high temperature environments 373
3 Numerical simulation of cylindrical specimen exposed to high temperature 376
Conclusions 378
References 378
Modelling the Glass Press-Blow Process 380
1 Introduction 380
2 Governing equations 380
3 Re-initialisation of the level set function 382
4 Results 383
5 Conclusions 384
References 384
Real-Time Control of Surface Remelting 385
1 Introduction 385
2 Local grid re.nement 386
3 Local defect correction 387
4 Simulations 388
References 389
Fast Shape Design for Industrial Components 390
1 Modeling the problem 390
2 A short sketch on the optimization strategy 391
3 Calculating the gradient for shape optimization 392
References 394
Modeling of Turbulence E.ects on Fiber Motion 395
1 Motivation 395
2 Fiber Dynamics 395
3 Construction of Fluctuating Flow Velocity 396
4 Stochastic Force Model 398
5 Numerical Results with White Noise 399
References 399
Design Optimisation of Wind-Loaded Cylindrical Silos Made from Composite Materials 400
1 Introduction 400
2 Silo Geometry, Wall Material Structure and Loading Conditions 401
3 Design Optimisation of The Cylindrical Section of The Silo 402
4 Example 403
5 Conclusions 404
References 404
Two-Dimensional Short Wave Stability Analysis of the Floating Process 405
1 Mathematical Formulation 405
2 The Disturbance System of Motion. 407
3 Short Wave Limit 408
References 409
Optimization in high-precision glass forming 410
1 Description of the forward problem 410
2 Optimization of the cooling curve 412
3 Identi.cation of the required initial geometry 414
References 414
A Mathematical Model for the Mechanical Etching of Glass 415
1 Introduction 415
2 Mathematical Model for Powder Erosion 415
3 Analytical Solution Method 416
4 Numerical Solution Method 418
References 419
FPM + Radiation = Mesh-Free Approach in Radiation Problems 420
1 Project 420
2 FPM 421
3 Radiation models 421
4 Results 424
References 424
Part VI Theme: Geophysics 426
Multiscale Methods and Streamline Simulation for Rapid Reservoir Performance Prediction 428
1 Introduction 428
2 Streamline Method 429
3 Multiscale Mixed Finite-Elements 430
4 Numerical Results 430
References 431
Part VII Theme: Financial Mathematics 434
ONE FOR ALL The Potential Approach to Pricing and Hedging 436
1 Introduction 436
2 Generalities about pricing 437
3 The potential approach 440
4 Markov processes and potentials 441
5 Foreign exchange in the potential approach 442
6 Markov chain potential models 443
7 Calibration 444
8 Evidence from bond data 446
9 Hedging 448
10 Conclusions and future directions 449
References 449
The Largest Claims Treaty ECOMOR 451
1 Introduction 451
2 Results 452
3 Conclusion and Remarks 455
References 455
American Options With Discrete Dividends Solved by Highly Accurate Discretizations 456
1 Black-Scholes Equation, Discretization 456
2 Numerical Results with Discrete Dividend 458
References 460
Semi-Lagrange Time Integration for PDE Models of Asian Options 461
1 Asian Options 461
2 Results 464
Fuzzy Binary Tree Model for European Options 466
1 Introduction 466
2 European-style Plain Vanilla Options in the Presence of Uncertainty 467
3 Solving Fuzzy Linear Systems 468
Effective Estimation of Banking Liquidity Risk 471
1 Introduction 471
2 Data Handling 472
3 Correlations 473
4 Conclusion 474
References 475
Part VIII Theme: Water Flow 477
Multiphase Flow and Transport Modeling in Heterogeneous Porous Media 478
1 Motivation 478
2 Scales and forces 482
3 Anisotropy at the pore scale 489
4 Dynamic Macroscale Model Formulation 494
5 Numerical Model 500
6 Examples 509
7 Conclusions 512
References 514
The Unsteady Expansion and Contraction of a Two- Dimensional Vapour Bubble Confined Between Superheated or Subcooled Plates 518
1 Introduction 518
2 Problem Formulation 519
3 Both Plates Superheated 520
4 Summary 521
Acknowledgement 522
References 522
Animating Water Waves Using Semi- Lagrangian Techniques 523
1 Introduction 523
2 Semi-Lagrangian Techniques 524
3 Numerical Results 525
References 527
A Filtered Renewal Process as a Model for a River Flow 528
1 Introduction 528
2 Filtered Renewal Process 529
3 An Application 530
4 Conclusion 532
References 532
A Parallel Finite Element Method for Convection- Diffusion Problems 533
1 The computational mesh 533
2 The parallel .nite element method 533
3 Load balance 534
References 536
Modelling The Flow And Solidification of a Thin Liquid Film on a Three- Dimensional Surface 537
1 Introduction 537
2 Mathematical model 537
4 Conclusions 541
References 541
Numerical Schemes for Degenerate Parabolic Problems 542
1 Introduction 542
2 The Numerical Approaches 543
References 546
Finite Element Modified Method of Characteristics for Shallow Water Flows: Application to the Strait of Gibraltar 547
1 Introduction 547
2 Formulation of FEMMOC 548
3 Preliminary Results 550
References 550
LDC with compact FD schemes for convection- diffusion equations 552
1 Introduction 552
2 Problem description and formulation of the LDC algorithm 553
3 High order compact schemes 554
4 Combination of LDC with HOCFD 555
5 Numerical results 556
A Finite-Dimensional Modal Modelling of Nonlinear Fluid Sloshing 557
1 Single-dominant Modal System 557
2 Local and Non-Local Bifurcation Analysis 559
References 561
Part IX Other Contributions 563
On the Reliability of Repairable Systems: Methods and Applications 564
1 Introduction 564
2 Repairable systems 565
3 Non-homogeneous Poisson processes 567
4 Examples 576
5 Discussion 580
References 580
New Schemes for Differential-Algebraic Stiff Systems. 583
1 Introduction 583
2 Accuracy control 584
3 Rosenbrock Schemes 585
References 586
Wavelet and Cepstrum Analyses of Leaks in Pipe Networks 588
1 Introduction 588
2 Theory 589
3 Experiment 590
4 Comparison between theory and experiment 590
5 Conclusions 592
References 592
Robust Design Using Computer Experiments 593
1 Introduction 593
2 The Piston Simulator 594
3 Robustness Strategies 594
4 Comparison Of Robustness Strategies on the Piston 595
References 597
Non-Classical Shocks for Buckley-Leverett: Degenerate Pseudo- Parabolic Regularisation 598
1 Introduction 598
2 Travelling waves 600
References 602
A Multi-scale Approach to Functional Signature Analysis for Product End- of-Life Management 603
1 Introduction 603
2 Experimental Setup 604
3 Wavelet Approach for Analysis of Stapler Motor Data 605
4 Conclusions 606
References 607
Aspects of Multirate Time Integration Methods in Circuit Simulation Problems 608
1 Introduction 608
2 Model Problem 610
3 Interface treatment .tting hierarchical sub-circuits 612
References 612
Exploiting Features for Finite Element Model Generation 614
1 Introduction 614
2 Analysis model preparation 615
3 Exploiting feature attributes for FE model preparation 616
4 Conclusion 617
References 618
Implicit Subgrid-Scale Models in Space-Time VMS Discretisations 619
1 Introduction 619
2 Discretisation 620
3 Burgers Test Case 620
4 Computed Results 621
Multiscale Change-Point Analysis of Inhomogeneous Poisson Processes Using Unbalanced Wavelet Decompositions 624
1 Introduction 624
2 Multiscale binning 625
3 Wavelet maxima 626
4 Unbalanced wavelet analysis 627
5 Elimination of false maxima and results 628
References 628
Robust Soft Sensors Based on Ensemble of Symbolic Regression- Based Predictors 629
1 Introduction 629
2 Ensemble of GP-generated Predictors in Soft Sensors 630
3 Application 632
4 Conclusions 632
References 633
Two-Dimensional Patterns in High Frequency Plasma Discharges 634
1 Introduction 634
2 Proposed Model 635
3 Derivation and Analysis of Amplitude Equations 635
4 Numerical Results and Conclusions 638
References 638
A Mathematical Model for the Motion of a Towed Pipeline Bundle 639
1 The Controlled Depth Tow Method (CDTM) 639
2 A Mathematical Model 640
3 Analytical Solutions 641
4 Summary 642
Acknowledgement 643
References 643
Operators and Criteria for Integrating FEA in the Design Workflow: Toward a Multi- Resolution Mechanical Model 645
1 Introduction 645
2 Simpli.cation operators 646
3 Mechanical criteria 647
4 Conclusion 649
References 649
Wavelet Analysis of Sound Signal in Fluid- filled Viscoelastic Pipes 650
1 Introduction 650
2 Experiment 651
3 Analysis and Results 651
4 Conclusions 653
References 654
Coarse-Grained Simulation and Bifurcation Analysis Using Microscopic Time- Steppers 655
1 Introduction 655
2 Patch Dynamics 656
3 Coarse-grained Numerical Bifurcation Analysis 657
4 Conclusions 658
References 659
Optimal Prediction in Molecular Dynamics 660
1 Problem Description 660
2 Optimal Prediction 661
3 Comparing Optimal Prediction to the Original System 663
4 Conclusions and Outlook 664
References 665
From CAD to CFD Meshes for Ship Geometries 666
1 Introduction 666
2 Chart surfaces 667
3 Examples and Future Work 669
References 670
Integration of Strongly Damped Mechanical Systems by Runge- Kutta Methods 671
1 Motivation 671
2 Expansion of the Analytical Solution 673
3 RadauIIA Methods 673
4 Error Results 674
References 675
Numerical Simulation of SMA Actuators 676
1 Introduction 676
2 Mathematical Model 677
3 Numerical Treatment 679
References 680
Color Plates 682
Author index 706

Fast Numerical Computing for a Family of Smooth Trajectories in Fluids Flow ( p. 39)

G. Argentini Riello Group, via degli Alpini 1, 37045 Legnago (Verona), Italy gianluca.argentini@riellogroup.com
Summary.

In this work I present a technique of construction and fast evaluation of a family of cubic polynomials for analytic smoothing and graphical rendering of particles trajectories for flows in a generic geometry. The principal result of the work was implementation and test of a method for interpolation of 3D points by regular parametric curves, and fast and efficient evaluation of these functions for a good resolution of rendering.

For this purpose I have used a parallel environment using a multiprocessor cluster architecture. The effciency of the used method is good, mainly reducing the number of floating-points computations by caching the numerical values of some line-parameter’s powers, and reducing the necessity of communication among processes. This work has been developed for the Research &, Development Department of my company for planning advanced customized models of industrial burners.
Key words:
computational fluid dynamics, cubic spline interpolation, parallel computing, parallel effciency.

1 Introduction

Industrial and power burners have some particular requirements, as a customized study of the geometry for combustion head and combustion chamber for an optimal shape of the flame. Rapid prototyping for an accurate design of the correct geometry involves a numerical simulation of the gas or oil flows in the burner’s components.

The necessity of an high graphic resolution requires a large amount of particles paths for tracing the streamlines of flow. Hence the numerical computation is memory and cpu very expensive for the used hardware environment. In a tipical simulation the number of paths to compute is some thousands, and the number of geometrical points to interpolate for each path is some thousands too. For the treatment of this large amount of data a parallel environment can be very useful.

2 Fitting trajectories with cubic polynomials
We suppose to have a dataset output from pre-processing and processing phases of a simulation, for example from numerical resolution of Navier-Stokes equations or from Cellular Automaton models [1].We would a fast and flexible method to obtain from those data an accurate paths tracking of fluid particles with a smooth 3D visualization of trajectories, possibly with continuous slope and curvature.

Our experience shows that Computational Fluid Dynamics packages have some limits in this post-processing phase, principally due to a rigid resolution of the initial mesh and to a small degree of parallelism. Let S the number of 3D points for each trajectory andMthe total number of trajectories from simulation dataset.

We have tested that usual interpolation methods have some disadvantages for our aims: for example Bezier-like is not realistic in case of twisting or diverging speed-fields, Chebychev or Least- Squares-like are too rigid for a customized application, polynomial flitting is simple but often shows spurious effects as Runge phenomenon [6]. We have elaborated a spline-based technique.