Progress in Industrial Mathematics at ECMI 2004

1. Auflage 2006
ISBN: 978-3-540-28073-6
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 678 Seiten

ECMI has a brand name in Industrial Mathematics and organises successful biannual conferences. This time, the conference on Industrial Mathematics held in Eindhoven in June 2004 Mathematics focused on Aerospace, Electronic Industry, Chemical Technology, Life Sciences, Materials, Geophysics, Financial Mathematics and Water flow. The majority of the invited talks on these topics can be found in these proceedings. Apart from these lectures, a large number of contributed papers and minisymposium papers are included here. They give an interesting (and impressive) overview of the important place mathematics has achieved in solving all kinds of problems met in industry, and commerce in particular.

Autoren/Hrsg.

Inhaltsverzeichnis

1;Preface;5
2;Contents;7
3;Part I Theme: Aerospace;31
3.1;The MEGAFLOW Project – Numerical Flow Simulation for Aircraft;32
3.1.1;1 Introduction;32
3.1.2;2 MEGAFLOW software;33
3.1.3;3 Software validation;42
3.1.4;4 Industrial Applications;45
3.1.5;5 Multidisciplinary simulations;52
3.1.6;6 Numerical optimization;54
3.1.7;7 Conclusions and perspective;58
3.1.8;References;59
3.2;Gradient Computations for Optimal Design of Turbine Blades;63
3.2.1;1 Introduction;63
3.2.2;2 Model Problem;63
3.2.3;3 Gradient Computation;65
3.2.4;4 Optimal Turbine Blade;66
3.2.5;References;67
3.3;Fast Numerical Computing for a Family of Smooth Trajectories in Fluids Flow;68
3.3.1;1 Introduction;68
3.3.2;2 Fitting trajectories with cubic polynomials;69
3.3.3;3 Computing splines;70
3.3.4;4 Valuating splines;70
3.3.5;5 Computing values of splines;72
3.3.6;6 Conclusions;72
3.3.7;References;72
3.4;Optimal Control of an ISS-Based Robotic Manipulator with Path Constraints;73
3.4.1;1 Introduction;73
3.4.2;2 Optimal Control Problem;74
3.4.3;3 Transformation into Minimum Coordinates;74
3.4.4;4 Optimal Control Theory;76
3.4.5;5 Numerical Example;77
3.4.6;References;77
3.5;Rigorous Analysis of Extremely Large Spherical Reflector Antennas: EM Case;78
3.5.1;1 Introduction;78
3.5.2;2 The Decoupled System at High Frequencies;79
3.5.3;3 Algorithm Performance on the Decoupled System;81
3.5.4;4 Conclusions;82
3.5.5;References;82
4;Part II Theme: Electronic Industry;84
4.1;Simulation and Measurement of Interconnects and On- Chip Passives: Gauge Fields and Ghosts as Numerical Tools;86
4.1.1;1 Introduction;86
4.1.2;2 The Maxwell Equations and the Drift-Di.usion Equations;88
4.1.3;3 Gauge Fields and Ghost Fields;90
4.1.4;4 Applications;94
4.1.5;5 Conclusions;101
4.1.6;References;102
4.2;Eigenvalue Problems in Surface Acoustic Wave Filter Simulations;103
4.2.1;1 Introduction;104
4.2.2;2 Problem Description and First Model Assumptions;106
4.2.3;3 The Piezoelectric Equations;108
4.2.4;4 A Scalar Model Problem;110
4.2.5;5 Piezoelectric Equations and Periodic Structures;116
4.2.6;6 Numerical Results;122
4.2.7;7 Conclusions;125
4.2.8;References;126
4.3;Diffraction Grating Theory with RCWA or the C Method;128
4.3.1;1 Introduction;128
4.3.2;2 Mathematical problem;129
4.3.3;3 Solution methods;129
4.3.4;4 Results;131
4.3.5;References;132
4.4;Relocation of Electric Field Domains and Switching Scenarios in Superlattices;133
4.4.1;1 Introduction;133
4.4.2;2 The Sequential Tunnelling Model;134
4.4.3;3 Switching Scenarios;135
4.4.4;References;137
4.5;Quantum Kinetic and Drift-Diffusion Equations for Semiconductor Superlattices;138
4.5.1;References;142
4.6;Model Order Reduction of Nonlinear Dynamical Systems;143
4.6.1;1 Introduction;143
4.6.2;2 Linear time-varying systems;144
4.6.3;3 Nonlinear systems;145
4.6.4;4 Illustrative numerical example;146
4.6.5;References;147
4.7;Electrolyte Flow and Temperature Calculations in Finite Cylinder Caused by Alternating Current;148
4.7.1;1 Introduction;148
4.7.2;2 Mathematical Model;149
4.7.3;3 The Finite-Di.erence Approximations and Numerical Results.;150
4.7.4;4 Conclusion;151
4.7.5;References;152
4.8;Numerical Simulation of the Problem Arising in the Gyrotron Theory;153
4.8.1;1 Introduction;153
4.8.2;2 Numerical Simulation;155
4.8.3;3 Conclusions;157
4.8.4;References;157
4.9;A Deterministic Multicell Solution to the Coupled Boltzmann- Poisson System Simulating the Transients of a 2D- Silicon MESFET;158
4.9.1;1 Introduction;158
4.9.2;2 Physical Assumptions;159
4.9.3;3 The Multicell Method for Spatially Two-Dimensional Problems;160
4.9.4;4 Numerical Results;161
4.10;Some Remarks on the Vector Fitting Iteration;163
4.10.1;1 Introduction;163
4.10.2;2 An iterative scheme for solving rational LS problems;164
4.10.3;3 The Vector Fitting methodology;165
4.10.4;4 How VF .ts in;165
4.10.5;5 Initial pole placement;167
4.10.6;References;167
4.11;Krylov Subspace Methods in the Electronic Industry;168
4.11.1;1 Introduction;168
4.11.2;2 Equation setting;169
4.11.3;3 Model Order Reduction;169
4.11.4;4 Validation of results;171
4.11.5;5 Redundancy;171
4.11.6;6 Conclusions;172
4.11.7;References;172
4.12;On Nonlinear Iteration Methods for DC Analysis of Industrial Circuits;173
4.12.1;1 Introduction;173
4.12.2;2 Equation formulation;174
4.12.3;3 Line-search methods;175
4.12.4;4 Trust-region methods;175
4.12.5;5 Non-monotone strategy;175
4.12.6;6 Dog-leg method;175
4.12.7;7 Tensor methods;176
4.12.8;8 Results;176
4.12.9;References;177
4.13;Implementing Efficient Array Traversing for FDTD- lumped Element Cosimulation;178
4.13.1;1 Introduction;178
4.13.2;2 Implementing the Data Types and Array Traversing;179
4.13.3;3 Comparison of the Two Data Types;180
4.14;Thermal Modeling of Bottle Glass Pressing;183
4.14.1;1 Introduction;183
4.14.2;2 Physical model;183
4.14.3;3 Finite element model;185
4.14.4;4 Results;186
4.14.5;5 Conclusions;187
4.14.6;References;187
4.15;Simulation of Pulsed Signals in MPDAE- Modelled SC- Circuits;188
4.15.1;1 Introduction;188
4.15.2;2 Switched capacitor .lter;188
4.15.3;3 Multidimensional approach;189
4.15.4;4 Miller integrator;191
4.15.5;5 Conclusions;192
4.15.6;References;192
4.16;A More Efficient Rigorous Coupled-Wave Analysis Algorithm;193
4.16.1;1 Introduction;193
4.16.2;2 The model;194
4.16.3;3 The equations and boundary conditions;195
4.16.4;4 Numerical results;197
4.16.5;5 Conclusions;197
4.16.6;References;197
4.17;Iterative Solution Approaches for the Piezoelectric Forward Problem;198
4.17.1;1 Introduction;198
4.17.2;2 Mathematical Model;199
4.17.3;3 Iterative Solution;199
4.17.4;4 Numerical Experiments;200
4.18;Hydrodynamic Modeling of an Ultra-Thin Base Silicon Bipolar Transistor;203
4.18.1;1 Introduction;203
4.18.2;2 The Extended Hydrodynamic Model;204
4.18.3;3 Limit Models;204
4.18.4;4 Numerical Results;205
4.18.5;References;207
4.19;Warped MPDAE Models with Continuous Phase Conditions;208
4.19.1;1 Introduction;208
4.19.2;2 Multivariate Signal Model;209
4.19.3;3 Warped MPDAE System;210
4.19.4;4 Numerical Simulation;210
4.19.5;5 Conclusions;212
4.19.6;References;212
4.20;Exact Closure Relations for the Maximum Entropy Moment System in Semiconductor Using Kane’s Dispersion Relation;213
4.20.1;1 The Maximum Entropy Moment Systems for Electrons in Semiconductors;213
4.20.2;2 Solvability of the Maximum Entropy Problem;215
4.20.3;3 The Euler-Poisson Model;216
4.20.4;References;217
4.21;Reduced Order Models for Eigenvalue Problems;218
4.21.1;1 Introduction;218
4.21.2;2 Reduced Order Modelling Problem;219
4.21.3;3 Reduced Order Modelling Methods;219
4.21.4;4 New Research Directions;221
4.21.5;References;222
4.22;DRK Methods for Time-Domain Oscillator Simulation;223
4.22.1;1 Introduction;223
4.22.2;2 DRK methods;223
4.22.3;3 Two-stage Example;225
4.22.4;4 Alternative Formulation;226
4.22.5;5 Conclusions;227
4.22.6;References;227
4.23;Digital Linear Control Theory Applied To Automatic Stepsize Control In Electrical Circuit Simulation;228
4.23.1;1 Introduction to error control;228
4.23.2;2 Control-Theoretic Approach to Stepsize Control;229
4.23.3;3 Derivation of Process Model for BDF-Methods;230
4.23.4;4 Design of Finite Order Digital Linear Stepsize Controller;230
4.23.5;5 Numerical Experiments;231
4.23.6;6 Conclusions;232
4.23.7;References;232
5;Part III Theme: Chemical Technology;234
5.1;On the Dynamics of a Bunsen Flame;236
5.1.1;1 Introduction;236
5.1.2;2 Flame front dynamics;236
5.1.3;3 Solution in the case of a Poiseuille .ow;237
5.1.4;4 Flame response to .ow perturbations;239
5.1.5;References;240
5.2;Index Analysis for Singular PDE Models of Fuel Cells;241
5.2.1;1 Time Index: De.nition and Prototype Example;241
5.2.2;2 Time Index of Dynamic Fuel Cell Models;243
5.2.3;References;245
5.3;On the Modeling of the Phase Separation of a Gelling Polymeric Mixture;246
5.3.1;1 Introduction;246
5.3.2;2 Theory;247
5.3.3;4 Conclusion;249
5.3.4;References;250
5.4;Iso-Surface Analysis of a Turbulent Diffusion Flame;251
5.4.1;1 Introduction;251
5.4.2;2 Di.usion .ame in a mixing layer;252
5.4.3;3 Iso-surface analysis of turbulent .ame properties;253
5.4.4;References;255
5.5;A Simplified Model for Non–Isothermal Crystallization of Polymers;256
5.5.1;1 Introduction;256
5.5.2;2 Temperature Equation with Memory;257
5.5.3;3 Numerical Results;258
5.6;Numerical Simulation of Cylindrical Induction Heating Furnaces;261
5.6.1;1 Introduction;261
5.6.2;2 Mathematical modelling;262
5.6.3;3 Numerical solution;264
5.6.4;References;265
5.7;Thermal Radiation E.ect on Thermal Explosion in a Gas Containing Evaporating Fuel Droplets.;266
5.7.1;1 Introduction;266
5.7.2;2 Physical model;267
5.7.3;3 Conclusions;270
5.7.4;References;270
5.8;Local Defect Correction for Laminar Flame Simulation;271
5.8.1;1 Introduction;271
5.8.2;2 An outline of LDC;271
5.8.3;3 Constructing an orthogonal curvilinear grid;273
5.8.4;4 The thermo-di.usive model for laminar .ames;274
5.8.5;References;275
5.9;Development of a Hierarchical Model Family for Molten Carbonate Fuel Cells with Direct Internal Reforming ( DIR- MCFC);276
5.9.1;Introduction;276
5.9.2;MCFC Working Principle;277
5.9.3;The Reference Model;278
5.9.4;Simulation Results and Model Applications;279
5.9.5;References;280
5.10;Modelling of Filtration and Regeneration Processes in Diesel Particulate Traps;281
5.10.1;1 Introduction;281
5.10.2;2 Simulation model;282
5.10.3;3 Results;284
5.10.4;4 Conclusion and Outlook;284
5.10.5;References;285
5.11;Modelling the Shelf Life of Packaged Olive Oil Stored at Various Conditions;286
5.11.1;1 Introduction;286
5.11.2;2 Experimental;287
5.11.3;3 Theory;287
5.11.4;4 Result and Discussion;288
5.11.5;5 Conclusion;290
5.11.6;References;290
5.12;Nonlinear Model Reduction of a Dynamic Two- dimensional Molten Carbonate Fuel Cell Model;291
5.12.1;1 Introduction;291
5.12.2;2 Spatially Distributed Reference Model of the MCFC;292
5.12.3;3 Derivation of the Reduced MCFC Model;292
5.12.4;4 Validation of the Reduced Model;294
5.12.5;5 Conclusions;295
5.12.6;References;295
5.13;Liquid/Solid Phase Change with Convection and Deformations: 2D Case;297
5.13.1;1 Introduction;297
5.13.2;2 Governing Equations and Reformulation;298
5.13.3;3 Numerical Test and Conclusions;299
5.14;Mathematical Modelling of Mass Transport Equations in Fixed- Bed Absorbers;302
5.14.1;1 Introduction;302
5.14.2;2 Dimensionless model;303
5.14.3;3 Application: Working Capacity test;306
5.14.4;4 Conclusions;306
5.14.5;References;306
5.15;Injection Vapour Model in a Porous Medium Accounting for a Weak Condensation;307
5.15.1;1 Motivating Problem and Mathematical Model;307
5.15.2;2 Comparisons with Experimental Data;310
5.15.3;References;311
5.16;Multigrid Solution of Three-Dimensional Radiative Heat Transfer in Glass Manufacturing;312
5.16.1;1 Introduction;312
5.16.2;2 Radiative Heat Transfer in Glass Manufacturing;313
5.16.3;3 Multigrid Solution Procedure;314
5.16.4;4 Results;315
5.16.5;References;316
5.17;DEM Simulations of the DI Toner Assembly;317
5.17.1;1 Introduction;317
5.17.2;2 Force Models;318
5.17.3;3 Results;320
5.17.4;4 Conclusion;320
5.17.5;References;321
5.18;Modeling of Drying Processes in Pore Networks;322
5.18.1;1 Introduction;322
5.18.2;2 Pore network modeling of drying without the presence of liquid . lms;323
5.18.3;3 The e.ect of liquid .lms;325
5.18.4;4 Conclusions;326
5.18.5;References;326
5.19;Mathematical Modelling of Flow through Pleated Cartridge Filters;327
5.19.1;Introduction;327
5.19.2;Mathematical Statement of the Combined Stokes/Darcy Flow Regimes;327
5.19.3;Results and Discussions;329
5.19.4;References;331
5.20;Comparison of Some Mixed Integer Non-linear Solution Approaches Applied to Process Plant Layout Problems;332
5.20.1;1 Introduction;332
5.20.2;2 Problem formulation;333
5.20.3;3 Non-Linear Solution Approaches;333
5.20.4;4 Illustrative examples;334
5.20.5;5 Conclusions;335
5.21;A Mathematical Model of Three-Dimensional Flow in a Scraped- Surface Heat Exchanger;337
5.21.1;1 Scraped-Surface Heat Exchangers (SSHEs);337
5.21.2;2 Transverse Flow;338
5.21.3;3 Longitudinal Flow;340
5.21.4;4 Summary;341
5.21.5;Acknowledgements;341
5.21.6;References;341
6;Part IV Theme: Life Sciences;343
6.1;Transmission Line Matrix Modeling of Sound Wave Propagation in Stationary and Moving Media;344
6.1.1;1 Introduction;344
6.1.2;2 TLM Model of Stationary Media;345
6.1.3;3 TLM Model of Moving Media;347
6.1.4;4 Conclusion;347
6.1.5;References;348
6.2;Viscous Drops Spreading With Evaporation And Applications To DNA Biochips;349
6.2.1;1 Introduction;349
6.2.2;2 The physical model and the lubrication approximation;350
6.2.3;References;353
6.3;Similarity-Based Object Recognition of Airborne Fungi in Digital Images;354
6.3.1;1 Introduction;354
6.3.2;2 Fungi Images;354
6.3.3;3 Similarity-Based Object Recognition;355
6.3.4;4 Results;357
6.3.5;5 Conclusions;358
6.3.6;References;358
6.4;Rivalling Optimal Control in Robot- Assisted Surgery;359
6.4.1;1 Introduction;359
6.4.2;2 Manipulator Model;360
6.4.3;3 Optimal Control;360
6.4.4;4 Optimal Control Constraints;361
6.4.5;5 Example: Constrained Motion and Rivalling Control;363
6.4.6;References;363
7;Part V Theme: Materials;365
7.1;A Multiphase Model for Concrete: Numerical Solutions and Industrial Applications;366
7.1.1;Physical and mathematical model;366
7.1.2;1 Numerical solution;369
7.1.3;Application of the model to young concrete;369
7.1.4;Numerical simulation of self-desiccation process;371
7.1.5;2 Application of the model to concrete structures in high temperature environments;373
7.1.6;3 Numerical simulation of cylindrical specimen exposed to high temperature;376
7.1.7;Conclusions;378
7.1.8;References;378
7.2;Modelling the Glass Press-Blow Process;380
7.2.1;1 Introduction;380
7.2.2;2 Governing equations;380
7.2.3;3 Re-initialisation of the level set function;382
7.2.4;4 Results;383
7.2.5;5 Conclusions;384
7.2.6;References;384
7.3;Real-Time Control of Surface Remelting;385
7.3.1;1 Introduction;385
7.3.2;2 Local grid re.nement;386
7.3.3;3 Local defect correction;387
7.3.4;4 Simulations;388
7.3.5;References;389
7.4;Fast Shape Design for Industrial Components;390
7.4.1;1 Modeling the problem;390
7.4.2;2 A short sketch on the optimization strategy;391
7.4.3;3 Calculating the gradient for shape optimization;392
7.4.4;References;394
7.5;Modeling of Turbulence E.ects on Fiber Motion;395
7.5.1;1 Motivation;395
7.5.2;2 Fiber Dynamics;395
7.5.3;3 Construction of Fluctuating Flow Velocity;396
7.5.4;4 Stochastic Force Model;398
7.5.5;5 Numerical Results with White Noise;399
7.5.6;References;399
7.6;Design Optimisation of Wind-Loaded Cylindrical Silos Made from Composite Materials;400
7.6.1;1 Introduction;400
7.6.2;2 Silo Geometry, Wall Material Structure and Loading Conditions;401
7.6.3;3 Design Optimisation of The Cylindrical Section of The Silo;402
7.6.4;4 Example;403
7.6.5;5 Conclusions;404
7.6.6;References;404
7.7;Two-Dimensional Short Wave Stability Analysis of the Floating Process;405
7.7.1;1 Mathematical Formulation;405
7.7.2;2 The Disturbance System of Motion.;407
7.7.3;3 Short Wave Limit;408
7.7.4;References;409
7.8;Optimization in high-precision glass forming;410
7.8.1;1 Description of the forward problem;410
7.8.2;2 Optimization of the cooling curve;412
7.8.3;3 Identi.cation of the required initial geometry;414
7.8.4;References;414
7.9;A Mathematical Model for the Mechanical Etching of Glass;415
7.9.1;1 Introduction;415
7.9.2;2 Mathematical Model for Powder Erosion;415
7.9.3;3 Analytical Solution Method;416
7.9.4;4 Numerical Solution Method;418
7.9.5;References;419
7.10;FPM + Radiation = Mesh-Free Approach in Radiation Problems;420
7.10.1;1 Project;420
7.10.2;2 FPM;421
7.10.3;3 Radiation models;421
7.10.4;4 Results;424
7.10.5;References;424
8;Part VI Theme: Geophysics;426
8.1;Multiscale Methods and Streamline Simulation for Rapid Reservoir Performance Prediction;428
8.1.1;1 Introduction;428
8.1.2;2 Streamline Method;429
8.1.3;3 Multiscale Mixed Finite-Elements;430
8.1.4;4 Numerical Results;430
8.1.5;References;431
9;Part VII Theme: Financial Mathematics;434
9.1;ONE FOR ALL The Potential Approach to Pricing and Hedging;436
9.1.1;1 Introduction;436
9.1.2;2 Generalities about pricing;437
9.1.3;3 The potential approach;440
9.1.4;4 Markov processes and potentials;441
9.1.5;5 Foreign exchange in the potential approach;442
9.1.6;6 Markov chain potential models;443
9.1.7;7 Calibration;444
9.1.8;8 Evidence from bond data;446
9.1.9;9 Hedging;448
9.1.10;10 Conclusions and future directions;449
9.1.11;References;449
9.2;The Largest Claims Treaty ECOMOR;451
9.2.1;1 Introduction;451
9.2.2;2 Results;452
9.2.3;3 Conclusion and Remarks;455
9.2.4;References;455
9.3;American Options With Discrete Dividends Solved by Highly Accurate Discretizations;456
9.3.1;1 Black-Scholes Equation, Discretization;456
9.3.2;2 Numerical Results with Discrete Dividend;458
9.3.3;References;460
9.4;Semi-Lagrange Time Integration for PDE Models of Asian Options;461
9.4.1;1 Asian Options;461
9.4.2;2 Results;464
9.5;Fuzzy Binary Tree Model for European Options;466
9.5.1;1 Introduction;466
9.5.2;2 European-style Plain Vanilla Options in the Presence of Uncertainty;467
9.5.3;3 Solving Fuzzy Linear Systems;468
9.6;Effective Estimation of Banking Liquidity Risk;471
9.6.1;1 Introduction;471
9.6.2;2 Data Handling;472
9.6.3;3 Correlations;473
9.6.4;4 Conclusion;474
9.6.5;References;475
10;Part VIII Theme: Water Flow;477
10.1;Multiphase Flow and Transport Modeling in Heterogeneous Porous Media;478
10.1.1;1 Motivation;478
10.1.2;2 Scales and forces;482
10.1.3;3 Anisotropy at the pore scale;489
10.1.4;4 Dynamic Macroscale Model Formulation;494
10.1.5;5 Numerical Model;500
10.1.6;6 Examples;509
10.1.7;7 Conclusions;512
10.1.8;References;514
10.2;The Unsteady Expansion and Contraction of a Two- Dimensional Vapour Bubble Confined Between Superheated or Subcooled Plates;518
10.2.1;1 Introduction;518
10.2.2;2 Problem Formulation;519
10.2.3;3 Both Plates Superheated;520
10.2.4;4 Summary;521
10.2.5;Acknowledgement;522
10.2.6;References;522
10.3;Animating Water Waves Using Semi- Lagrangian Techniques;523
10.3.1;1 Introduction;523
10.3.2;2 Semi-Lagrangian Techniques;524
10.3.3;3 Numerical Results;525
10.3.4;References;527
10.4;A Filtered Renewal Process as a Model for a River Flow;528
10.4.1;1 Introduction;528
10.4.2;2 Filtered Renewal Process;529
10.4.3;3 An Application;530
10.4.4;4 Conclusion;532
10.4.5;References;532
10.5;A Parallel Finite Element Method for Convection- Diffusion Problems;533
10.5.1;1 The computational mesh;533
10.5.2;2 The parallel .nite element method;533
10.5.3;3 Load balance;534
10.5.4;References;536
10.6;Modelling The Flow And Solidification of a Thin Liquid Film on a Three- Dimensional Surface;537
10.6.1;1 Introduction;537
10.6.2;2 Mathematical model;537
10.6.3;4 Conclusions;541
10.6.4;References;541
10.7;Numerical Schemes for Degenerate Parabolic Problems;542
10.7.1;1 Introduction;542
10.7.2;2 The Numerical Approaches;543
10.7.3;References;546
10.8;Finite Element Modified Method of Characteristics for Shallow Water Flows: Application to the Strait of Gibraltar;547
10.8.1;1 Introduction;547
10.8.2;2 Formulation of FEMMOC;548
10.8.3;3 Preliminary Results;550
10.8.4;References;550
10.9;LDC with compact FD schemes for convection- diffusion equations;552
10.9.1;1 Introduction;552
10.9.2;2 Problem description and formulation of the LDC algorithm;553
10.9.3;3 High order compact schemes;554
10.9.4;4 Combination of LDC with HOCFD;555
10.9.5;5 Numerical results;556
10.10;A Finite-Dimensional Modal Modelling of Nonlinear Fluid Sloshing;557
10.10.1;1 Single-dominant Modal System;557
10.10.2;2 Local and Non-Local Bifurcation Analysis;559
10.10.3;References;561
11;Part IX Other Contributions;563
11.1;On the Reliability of Repairable Systems: Methods and Applications;564
11.1.1;1 Introduction;564
11.1.2;2 Repairable systems;565
11.1.3;3 Non-homogeneous Poisson processes;567
11.1.4;4 Examples;576
11.1.5;5 Discussion;580
11.1.6;References;580
11.2;New Schemes for Differential-Algebraic Stiff Systems.;583
11.2.1;1 Introduction;583
11.2.2;2 Accuracy control;584
11.2.3;3 Rosenbrock Schemes;585
11.2.4;References;586
11.3;Wavelet and Cepstrum Analyses of Leaks in Pipe Networks;588
11.3.1;1 Introduction;588
11.3.2;2 Theory;589
11.3.3;3 Experiment;590
11.3.4;4 Comparison between theory and experiment;590
11.3.5;5 Conclusions;592
11.3.6;References;592
11.4;Robust Design Using Computer Experiments;593
11.4.1;1 Introduction;593
11.4.2;2 The Piston Simulator;594
11.4.3;3 Robustness Strategies;594
11.4.4;4 Comparison Of Robustness Strategies on the Piston;595
11.4.5;References;597
11.5;Non-Classical Shocks for Buckley-Leverett: Degenerate Pseudo- Parabolic Regularisation;598
11.5.1;1 Introduction;598
11.5.2;2 Travelling waves;600
11.5.3;References;602
11.6;A Multi-scale Approach to Functional Signature Analysis for Product End- of-Life Management;603
11.6.1;1 Introduction;603
11.6.2;2 Experimental Setup;604
11.6.3;3 Wavelet Approach for Analysis of Stapler Motor Data;605
11.6.4;4 Conclusions;606
11.6.5;References;607
11.7;Aspects of Multirate Time Integration Methods in Circuit Simulation Problems;608
11.7.1;1 Introduction;608
11.7.2;2 Model Problem;610
11.7.3;3 Interface treatment .tting hierarchical sub-circuits;612
11.7.4;References;612
11.8;Exploiting Features for Finite Element Model Generation;614
11.8.1;1 Introduction;614
11.8.2;2 Analysis model preparation;615
11.8.3;3 Exploiting feature attributes for FE model preparation;616
11.8.4;4 Conclusion;617
11.8.5;References;618
11.9;Implicit Subgrid-Scale Models in Space-Time VMS Discretisations;619
11.9.1;1 Introduction;619
11.9.2;2 Discretisation;620
11.9.3;3 Burgers Test Case;620
11.9.4;4 Computed Results;621
11.10;Multiscale Change-Point Analysis of Inhomogeneous Poisson Processes Using Unbalanced Wavelet Decompositions;624
11.10.1;1 Introduction;624
11.10.2;2 Multiscale binning;625
11.10.3;3 Wavelet maxima;626
11.10.4;4 Unbalanced wavelet analysis;627
11.10.5;5 Elimination of false maxima and results;628
11.10.6;References;628
11.11;Robust Soft Sensors Based on Ensemble of Symbolic Regression- Based Predictors;629
11.11.1;1 Introduction;629
11.11.2;2 Ensemble of GP-generated Predictors in Soft Sensors;630
11.11.3;3 Application;632
11.11.4;4 Conclusions;632
11.11.5;References;633
11.12;Two-Dimensional Patterns in High Frequency Plasma Discharges;634
11.12.1;1 Introduction;634
11.12.2;2 Proposed Model;635
11.12.3;3 Derivation and Analysis of Amplitude Equations;635
11.12.4;4 Numerical Results and Conclusions;638
11.12.5;References;638
11.13;A Mathematical Model for the Motion of a Towed Pipeline Bundle;639
11.13.1;1 The Controlled Depth Tow Method (CDTM);639
11.13.2;2 A Mathematical Model;640
11.13.3;3 Analytical Solutions;641
11.13.4;4 Summary;642
11.13.5;Acknowledgement;643
11.13.6;References;643
11.14;Operators and Criteria for Integrating FEA in the Design Workflow: Toward a Multi- Resolution Mechanical Model;645
11.14.1;1 Introduction;645
11.14.2;2 Simpli.cation operators;646
11.14.3;3 Mechanical criteria;647
11.14.4;4 Conclusion;649
11.14.5;References;649
11.15;Wavelet Analysis of Sound Signal in Fluid- filled Viscoelastic Pipes;650
11.15.1;1 Introduction;650
11.15.2;2 Experiment;651
11.15.3;3 Analysis and Results;651
11.15.4;4 Conclusions;653
11.15.5;References;654
11.16;Coarse-Grained Simulation and Bifurcation Analysis Using Microscopic Time- Steppers;655
11.16.1;1 Introduction;655
11.16.2;2 Patch Dynamics;656
11.16.3;3 Coarse-grained Numerical Bifurcation Analysis;657
11.16.4;4 Conclusions;658
11.16.5;References;659
11.17;Optimal Prediction in Molecular Dynamics;660
11.17.1;1 Problem Description;660
11.17.2;2 Optimal Prediction;661
11.17.3;3 Comparing Optimal Prediction to the Original System;663
11.17.4;4 Conclusions and Outlook;664
11.17.5;References;665
11.18;From CAD to CFD Meshes for Ship Geometries;666
11.18.1;1 Introduction;666
11.18.2;2 Chart surfaces;667
11.18.3;3 Examples and Future Work;669
11.18.4;References;670
11.19;Integration of Strongly Damped Mechanical Systems by Runge- Kutta Methods;671
11.19.1;1 Motivation;671
11.19.2;2 Expansion of the Analytical Solution;673
11.19.3;3 RadauIIA Methods;673
11.19.4;4 Error Results;674
11.19.5;References;675
11.20;Numerical Simulation of SMA Actuators;676
11.20.1;1 Introduction;676
11.20.2;2 Mathematical Model;677
11.20.3;3 Numerical Treatment;679
11.20.4;References;680
12;Color Plates;682
13;Author index;706

Leseproben

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 [e-mail]
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.