Vuik / Koren Advanced Computational Methods in Science and Engineering

1. Auflage 2009
ISBN: 978-3-642-03344-5
Verlag: Springer
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 498 Seiten

The aim of the present book is to show, in a broad and yet deep way, the state of the art in computational science and engineering. Examples of topics addressed are: fast and accurate numerical algorithms, model-order reduction, grid computing, immersed-boundary methods, and specific computational methods for simulating a wide variety of challenging problems, problems such as: fluid-structure interaction, turbulent flames, bone-fracture healing, micro-electro-mechanical systems, failure of composite materials, storm surges, particulate flows, and so on. The main benefit offered to readers of the book is a well-balanced, up-to-date overview over the field of computational science and engineering, through in-depth articles by specialists from the separate disciplines.

Autoren/Hrsg.

Vuik, Kees

Koren, Barry

Inhaltsverzeichnis

1;Foreword;5
2;Preface by the editors;6
3;Contents;8
4;A Model-Order Reduction Approach toParametric Electromagnetic Inversion;10
4.1;1 Introduction;10
4.2;2 Integral representations and their discretized counterparts;12
4.3;3 Reduced-order models for the scattered field;15
4.4;4 The reduced-order model objective function;18
4.4.1;4.1 Multiple frequencies;20
4.5;5 Numerical experiments;21
4.6;References;28
5;Shifted-Laplacian Preconditioners for Heterogeneous Helmholtz Problems;29
5.1;1 Introduction;29
5.2;2 The Helmholtz equation and a seismic application;31
5.2.1;2.1 Mathematical problem definition;32
5.2.2;2.2 Discretization;34
5.2.2.1;2.2.1 Validation of the discretization;35
5.3;3 Iterative solution method;36
5.3.1;3.1 Multigrid for the Helmholtz equation;37
5.3.2;3.2 Shifted Laplacian preconditioned Krylov subspace method;38
5.3.3;3.3 Fourier analysis;39
5.3.4;3.4 Multigrid preconditioner;43
5.3.5;3.5 AMG type interpolation;44
5.4;4 Numerical experiments;46
5.4.1;4.1 Homogeneous problem;46
5.4.1.1;4.1.1 Second- and fourth-order discretizations;46
5.4.1.2;4.1.2 Fixed wavenumber, increasing mesh sizes;48
5.4.2;4.2 The wedge problem;49
5.4.3;4.3 The Sigsbee problem;49
5.5;5 Conclusion;51
5.6;Acknowledgment;51
5.7;References;52
6;On Numerical Issues in Time Accurate LaminarReacting Gas Flow Solvers;55
6.1;1 Introduction;56
6.2;2 Numerical modeling of chemical vapor deposition;57
6.2.1;2.1 Transport model for the gas species;59
6.2.2;2.2 Modeling of surface chemistry;60
6.3;3 Chemistry models;61
6.3.1;3.1 Chemistry model I: 7 species and 5 gas phase reactions;61
6.3.2;3.2 Chemistry model II: 17 species and 26 gas phase reactions;63
6.4;4 Numerical difficulties;65
6.4.1;4.1 Positivity conservation of mass fractions;65
6.4.1.1;4.1.1 Positive time integration;66
6.4.1.2;4.1.2 Positivity for Euler Forward (EF) and Euler Backward (EB);67
6.4.1.3;4.1.3 Positive time integration continued: general remarks;68
6.4.2;4.2 Comparison of some stiff ODE methods;68
6.4.2.1;4.2.1 Numerical results;70
6.5;5 Design of the Euler Backward solver;73
6.5.1;5.1 Globalized Inexact Projected Newton methods;73
6.5.2;5.2 Preconditioned Krylov solver;74
6.6;6 Numerical results;76
6.6.1;6.1 Discussion on the integration statistics;77
6.6.2;6.2 Model validation and time accurate solutions;79
6.7;7 Conclusions;82
6.8;References;85
7;Parallel Scientific Computing on LooselyCoupled Networks of Computers;87
7.1;1 Introduction;88
7.2;2 The problem;89
7.3;3 The basics: iterative methods;91
7.3.1;3.1 Simple iterations;92
7.3.2;3.2 Impatient processors: asynchronism;93
7.4;4 Acceleration: subspace methods;95
7.4.1;4.1 Hybrid methods: best of both worlds;97
7.4.2;4.2 Some experimental results;99
7.5;5 Efficient numerical algorithms in Grid computing;100
7.5.1;5.1 Grid middleware;101
7.5.1.1;5.1.1 Brief description of GridSolve;101
7.5.1.2;5.1.2 Brief description of CRAC;103
7.5.2;5.2 Target hardware;104
7.5.3;5.3 Parallel iterative methods: building blocks revisited;105
7.5.3.1;5.3.1 Matrix–vectormultiplication;105
7.5.3.2;5.3.2 Vector operations;106
7.5.3.3;5.3.3 Preconditioning step;107
7.5.3.4;5.3.4 Convergence detection;107
7.5.4;5.4 Applications;108
7.5.5;5.5 Advanced techniques;108
7.6;6 Concluding remarks and further reading;109
7.7;References;111
8;Data Assimilation Algorithms for Numerical Models;115
8.1;1 Introduction;115
8.2;2 Variational data assimilation;117
8.2.1;2.1 Data assimilation formulated as a minimization problem;117
8.2.2;2.2 The adjoint model;118
8.2.3;2.3 Discussion;119
8.3;3 Kalman filtering;120
8.3.1;3.1 The linear Kalman filter;120
8.3.2;3.2 Kalman filtering for large-scale systems;122
8.3.2.1;3.2.1 Square root filtering;122
8.3.2.2;3.2.2 Classical Ensemble Kalman filter;123
8.3.2.3;3.2.3 Reduced Rank Square Root Kalman filter;124
8.3.2.4;3.2.4 Discussion;126
8.4;4 A software environment for data assimilation: COSTA;127
8.4.1;4.1 COSTA components;128
8.4.2;4.2 The COSTA software;129
8.5;5 Applications in coastal sea modeling;131
8.5.1;5.1 Storm surge prediction using Kalman filtering;131
8.5.2;5.2 Using an RRSQRT Kalman filter to assimilate HF radar datainto a 3D coastal ocean model;135
8.5.2.1;5.2.1 Introduction;135
8.5.2.2;5.2.2 The TRIWAQ model for the IJmond region;136
8.5.2.3;5.2.3 Kalman filtering for large 3D models;138
8.5.2.4;5.2.4 Results;140
8.6;6 Applications in atmospheric chemistry modeling;140
8.6.1;6.1 Eulerian chemistry transport model EUROS;141
8.6.2;6.2 State space representation;141
8.6.3;6.3 Ground based observations;142
8.6.4;6.4 Results;143
8.6.5;6.5 Performance of RRSQRT algorithm, ENKF algorithm andCOFFEE (Complementary Orthogonal subspace Filter ForEfficient Ensembles) algorithm;145
8.7;7 Conclusions;146
8.8;References;148
9;Radial Basis Functions for InterfaceInterpolation and Mesh Deformation;151
9.1;1 Introduction;151
9.2;2 Non-matching meshes;152
9.2.1;2.1 Conservative and consistent coupling approach;153
9.2.1.1;2.1.1 Conservative approach;154
9.2.1.2;2.1.2 Consistent approach;155
9.2.2;2.2 Radial basis function interpolation (RBFI);156
9.2.3;2.2.1 Radial basis functions;157
9.2.4;2.2.2 Conservative approach;158
9.2.5;2.3 Analytical test problems;159
9.2.5.1;2.3.1 Transferring a smooth field;161
9.2.5.2;2.3.2 Transferring a non-smooth field;162
9.2.6;2.4 Quasi-1D FSI problem;164
9.2.6.1;2.4.1 Flow equations;165
9.2.6.2;2.4.2 Structure equations;165
9.2.6.3;2.4.3 Coupling procedure;166
9.2.6.4;2.4.4 Results;166
9.3;3 Mesh movement based on radial basis function interpolation;168
9.3.1;3.1 Radial basis function interpolation;169
9.3.2;3.2 Mesh quality metrics;172
9.3.3;3.3 2D mesh movement;173
9.3.3.1;3.3.1 Test case 1: Rotation and translation;173
9.3.3.2;3.3.2 Test case 2: Rigid body Rotation;176
9.3.3.3;3.3.3 Test case 3: Airfoil flap;177
9.3.3.4;3.3.4 Test case 4: Flow around airfoil;178
9.3.4;3.4 Importance of smooth mesh deformation for higher ordertime-integration;179
9.3.5;3.5 3D mesh deformation;181
9.3.6;3.6 Rotation and translation of 3D block;181
9.3.6.1;3.6.1 Flutter of the AGARD 445.6 wing;182
9.4;4 Conclusions;183
9.5;References;184
10;Least-Squares Spectral Element Methods inComputational Fluid Dynamics;187
10.1;1 Introduction;187
10.2;2 The least-squares formulation;188
10.2.1;2.1 Rayleigh-Ritz method;188
10.2.2;2.2 Galerkin formulations;191
10.2.3;2.3 Least-squares formulation;192
10.3;3 Spectral element methods;194
10.4;4 Convergence and a priori error estimates;195
10.5;5 Incompressible flows;198
10.5.1;5.1 Governing equations;198
10.5.2;5.2 The first order formulation of the Navier-Stokes equations;199
10.5.3;5.3 Linearization of the non-linear terms;199
10.5.4;5.4 Steady flow around a cylinder at low Reynolds;200
10.5.5;5.5 Comparison of numerical data with experimental data;201
10.5.5.1;5.5.1 S/d: LSQSEM vs. Experiment;201
10.5.6;5.6 Unsteady flow around a cylinder at low Reynolds;205
10.5.6.1;5.6.1 Outflow boundary condition;205
10.5.6.2;5.6.2 Base pressure coefficient;206
10.5.6.3;5.6.3 Drag and lift coefficients;207
10.6;6 Compressible flows;208
10.6.1;6.1 Compressible flow over a circular bump;209
10.6.1.1;6.1.1 General geometry and boundary conditions;209
10.6.1.2;6.1.2 Results for transonic flow;211
10.6.1.3;6.1.3 Results for supersonic flow;213
10.7;7 Miscellaneous topics;214
10.7.1;7.1 hp-adaptive LSQSEM;214
10.7.1.1;7.1.1 The mortar element method;214
10.7.1.2;7.1.2 The error estimator;215
10.7.1.3;7.1.3 Estimation of the Sobolev regularity;216
10.7.1.4;7.1.4 Application to the space-time linear advection equation;218
10.7.1.5;7.1.5 Illustration of an hp-adaptive strategy;219
10.7.2;7.2 Direct Minimization;220
10.7.2.1;7.2.1 Conventional least-squares finite element method;220
10.7.2.2;7.2.2 DirectMinimization - LSQSEM-DM;221
10.7.2.3;7.2.3 Global QR;223
10.7.2.4;7.2.4 The Poisson equation;224
10.7.3;7.3 Application of LSQSEM to viscoelastic fluids;227
10.8;8 Further reading;231
10.9;References;231
11;Finite-Volume Discretizations and ImmersedBoundaries;236
11.1;1 Introduction;236
11.2;2 Model equation and target problems;239
11.2.1;2.1 Standard finite-volume discretization;240
11.2.2;2.2 Initial and boundary conditions;240
11.2.3;2.3 Standard finite-volume schemes;241
11.3;3 Fluxes with embedded moving-boundary conditions;246
11.3.1;3.1 Higher-order accurate embedded-boundary fluxes;247
11.3.1.1;3.1.1 Cell-face states;247
11.3.1.2;3.1.2 Net cell fluxes;249
11.3.2;3.2 Spatial monotonicity domains and limiters;254
11.3.3;3.2.1 Spatial monotonicity domain and limiter for cell-face state ;254
11.3.4;3.2.2 Limiter for cell-face state;256
11.3.5;3.2.3 Spatial monotonicity domain and limiter for cell-face state;256
11.4;4 Temporal discretization;258
11.4.1;4.1 TVD conditions and time step;259
11.4.1.1;4.1.1 TVD conditions for limiter function;261
11.4.1.2;4.1.2 TVD conditions for limiter function;263
11.4.2;4.2 Local adaptivity in time;267
11.5;5 Numerical examples;270
11.6;6 Extension to more general cases;271
11.6.1;6.1 Extension to higher dimensions;272
11.6.2;6.2 Higher-order accuracy in time;272
11.7;7 Conclusion;273
11.8;Appendix;273
11.9;References;274
12;Large Eddy Simulation of TurbulentNon-Premixed Jet Flames with a High OrderNumerical Method;276
12.1;1 Introduction;276
12.2;2 Governing equations;278
12.3;3 Chemistry model;280
12.4;4 Numerical method;281
12.4.1;4.1 The derivative;282
12.4.2;4.2 Time discretization;285
12.4.3;4.3 The discretization of the Navier-Stokes equations for theSANDIA flame D problem;285
12.5;5 Boundary conditions;287
12.5.1;5.1 Parallel implementation;288
12.6;6 Simulation details;289
12.7;7 Summary and conclusions;293
12.8;8 Acknowledgements;293
12.9;References;293
13;A Suite of Mathematical Models for BoneIngrowth, Bone Fracture Healing andIntra-Osseous Wound Healing;295
13.1;1 Introduction;296
13.2;2 The bone-ingrowth model;298
13.2.1;2.1 The mechanical model;299
13.2.1.1;2.1.1 The elasticity domain;301
13.2.1.2;2.1.2 The porous tantalum;302
13.2.2;2.2 The biological part;303
13.2.3;2.3 The numerical method for the ingrowth model;306
13.2.4;2.4 Numerical experiments on the ingrowth model;309
13.3;3 The fracture healing model due to Bailon-Plaza;311
13.4;4 The model due to Adam;314
13.4.1;4.1 The model equations;315
13.5;5 Conclusions;316
13.6;References;317
14;Numerical Modeling of the ElectromechanicalInteraction in MEMS;321
14.1;1 Introduction;321
14.1.1;1.1 Electromechanical coupling;322
14.1.2;1.2 A one-dimensional example;324
14.1.3;1.3 Numerical modeling;327
14.2;2 Solution techniques;329
14.3;3 Finding the pull-in curve;331
14.3.1;3.1 Voltage stepping;331
14.3.2;3.2 Path following methods;332
14.3.3;3.3 Displacement stepping;334
14.3.4;3.4 Charge stepping;335
14.3.5;3.5 General remarks;337
14.3.6;3.6 Example;338
14.4;4 Coupled eigenfrequencies;341
14.4.1;4.1 Staggered method;342
14.4.2;4.2 Monolithic method;343
14.4.3;4.3 Example;344
14.5;5 Summary and conclusions;346
14.6;References;346
15;Simulation of Progressive Failure in CompositeLaminates;349
15.1;1 Introduction;349
15.2;2 Continuum damage;352
15.2.1;2.1 Material degradation;353
15.2.2;2.2 Consistent tangent;355
15.2.3;2.3 Regularization;356
15.2.4;2.4 Notched plate;358
15.2.5;2.5 Off-axis tensile test;362
15.3;3 Phantom node method;365
15.3.1;3.1 Kinematical and equilibrium relations;365
15.3.2;3.2 Crack propagation;367
15.3.3;3.3 Cohesive law;368
15.3.4;3.4 Consistent tangent;372
15.3.5;3.5 Off-axis tensile test;372
15.4;4 Conclusions;374
15.5;Acknowledgments;375
15.6;References;375
16;Numerical Modeling of Wave Propagation,Breaking and Run-Up on a Beach;378
16.1;1 Introduction;378
16.2;2 Governing equations;382
16.3;3 Numerical framework;384
16.3.1;3.1 Space discretization;384
16.3.1.1;3.1.1 Grid schematization;384
16.3.1.2;3.1.2 Location of grid variables;385
16.3.1.3;3.1.3 Space discretization of global continuity equation;387
16.3.1.4;3.1.4 Space discretization of local continuity equation;387
16.3.1.5;3.1.5 Space discretization of horizontal momentum equation;388
16.3.1.6;3.1.6 Space discretization of vertical momentum equation;389
16.3.2;3.2 Time integration;390
16.3.3;3.3 Solution method;392
16.4;4 Numerical experiments;395
16.4.1;4.1 Regular wave breaking on a slope;396
16.4.2;4.2 Periodic wave run-up on a planar beach;397
16.4.3;4.3 Regular breaking waves over a submerged bar;398
16.4.4;4.4 Irregular wave breaking in a laboratory barred surf zone;399
16.4.5;4.5 Deformation of waves by an elliptic shoal on sloped bottom;401
16.5;5 Conclusions;404
16.6;References;405
17;Hybrid Navier-Stokes/DSMC Simulations of GasFlows with Rarefied-Continuum Transitions;407
17.1;1 Introduction;407
17.2;2 From Boltzmann to Navier-Stokes;410
17.3;3 The hybrid numerical method;413
17.3.1;3.1 Introduction;413
17.3.2;3.2 Finite volume scheme for compressible Navier-Stokesequations;413
17.3.2.1;3.2.1 Finite volume discretization;413
17.3.2.2;3.2.2 Time discretization;414
17.3.2.3;3.2.3 The MUSCL discretization scheme;415
17.3.2.4;3.2.4 Chapman-Enskog split fluxes;415
17.3.3;3.3 Direct Simulation Monte Carlo scheme for rarefied gas flowsimulations;417
17.3.3.1;3.3.1 Initialization;418
17.3.3.2;3.3.2 Particle movement;418
17.3.3.3;3.3.3 Particle collisions;419
17.3.3.4;3.3.4 Sampling;421
17.3.4;3.4 Dynamic coupling of Navier-Stokes and DSMC solvers;422
17.3.4.1;3.4.1 Breakdown parameter;422
17.3.4.2;3.4.2 Steady-state formulation;422
17.3.4.3;3.4.3 Unsteady formulation;424
17.4;4 Results and discussion;425
17.4.1;4.1 Unsteady shock-tube problem;425
17.4.1.1;4.1.1 Sensitivity to numerical parameters;428
17.4.2;4.2 Rarefied Poiseuille flow;430
17.4.3;4.3 Steady-state jet expanding in a low pressure chamber;433
17.5;5 Conclusion;437
17.6;References;438
18;Multi-Scale PDE-Based Design of HierarchicallyStructured Porous Catalysts;440
18.1;1 Introduction;441
18.2;2 Implementation framework;441
18.3;3 PDE-based design of hierarchically structured porous catalysts;444
18.4;4 Conclusions;453
18.5;References;454
19;From Molecular Dynamics and ParticleSimulations towards Constitutive Relations forContinuum Theory;456
19.1;1 Introduction;457
19.2;2 The soft particle molecular dynamics method;457
19.2.1;2.1 Discrete particle model;458
19.2.2;2.2 Equations of motion;458
19.2.3;2.3 Normal contact force laws;459
19.2.3.1;2.3.1 Linear normal contact model;459
19.2.3.2;2.3.2 Adhesive, elasto-plastic normal contact model;460
19.2.3.3;2.3.3 Long range normal forces;461
19.2.4;2.4 Tangential forces and torques in general;462
19.2.4.1;2.4.1 Sliding;462
19.2.4.2;2.4.2 Objectivity;462
19.2.4.3;2.4.3 Rolling;463
19.2.4.4;2.4.4 Torsion;464
19.2.4.5;2.4.5 Summary;464
19.2.5;2.5 The tangential force- and torque-models;464
19.2.5.1;2.5.1 Sliding/sticking friction model;464
19.2.5.2;2.5.2 Rolling resistance model;466
19.2.5.3;2.5.3 Torsion resistance model;466
19.2.6;2.6 Background friction;466
19.2.7;2.7 Example: tension test simulation results;467
19.2.7.1;2.7.1 Model parameters for tension;468
19.2.7.2;2.7.2 Compressive and tensile strength;470
19.3;3 Hard sphere molecular dynamics;471
19.3.1;3.1 Smooth hard sphere collision model;472
19.3.2;3.2 Event-driven algorithm;472
19.4;4 The link between ED and DEM via the TC model;474
19.5;5 The stress in particle simulations;476
19.5.1;5.1 Dynamic stress;476
19.5.2;5.2 Static stress from virtual displacements;476
19.5.3;5.3 Stress for soft and hard spheres;477
19.6;6 2D simulation results;477
19.6.1;6.1 The equation of state from ED;478
19.6.2;6.2 Quasi-static DEM simulations;479
19.6.2.1;6.2.1 Model parameters;480
19.6.2.2;6.2.2 Boundary conditions;480
19.6.2.3;6.2.3 Initial configuration and compression;481
19.6.2.4;6.2.4 Compression and dilation;481
19.6.2.5;6.2.5 Stress tensor;483
19.7;7 Larger computational examples;485
19.7.1;7.1 Free cooling and cluster growth (ED);485
19.7.1.1;7.1.1 Initial configuration;485
19.7.1.2;7.1.2 System evolution;486
19.7.1.3;7.1.3 Discussion;487
19.7.2;7.2 3D (ring) shear cell simulation;487
19.7.2.1;7.2.1 Model system;487
19.7.2.2;7.2.2 Material and system parameters;488
19.7.2.3;7.2.3 Shear deformation results;488
19.7.2.4;7.2.4 Discussion;491
19.8;8 Conclusion;492
19.9;References;492
20;Editorial Policy;496
21;General Remarks;497
22;Lecture Notes in Computational Scienceand Engineering;498
23;Monographs in Computational Scienceand Engineering;500
24;Texts in Computational Scienceand Engineering;501