Handbook of numerical analysis: Volume 18 Handbook of numerical methods for hyperbolic problems : applied and modern issues
Gespeichert in:
| Weitere beteiligte Personen: | , , |
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| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Amsterdam
North-Holland
[2017]
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| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029599069&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | xix, 589 Seiten Illustrationen, Diagramme (teilweise farbig) |
| ISBN: | 9780444639103 |
Internformat
MARC
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| 245 | 1 | 0 | |a Handbook of numerical analysis |n Volume 18 |p Handbook of numerical methods for hyperbolic problems : applied and modern issues |c general editor: P. G. Ciarlet (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie), J. L. Lions |
| 264 | 1 | |a Amsterdam |b North-Holland |c [2017] | |
| 300 | |a xix, 589 Seiten |b Illustrationen, Diagramme (teilweise farbig) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 655 | 7 | |0 (DE-588)4143413-4 |a Aufsatzsammlung |2 gnd-content | |
| 700 | 1 | |a Abgrall, Rémi |0 (DE-588)1052897819 |4 edt | |
| 700 | 1 | |a Ciarlet, Philippe G. |d 1938- |e Sonstige |0 (DE-588)143368362 |4 oth | |
| 700 | 1 | |a Shu, Chi-Wang |d 1957- |0 (DE-588)1018436952 |4 edt | |
| 700 | 1 | |a Lions, Jacques-Louis |d 1928-2001 |e Sonstige |0 (DE-588)124055397 |4 oth | |
| 700 | 1 | |a Du, Qiang |d 1964- |0 (DE-588)1188249320 |4 edt | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-029599069 | |
Datensatz im Suchindex
| _version_ | 1819291017886564352 |
|---|---|
| adam_text | Contents
Contributors xv
Editors Introduction xvii
1. Cut Cells: Meshes and Solvers 1
M. Berger
1 Introduction 1
2 Brief Early History 3
3 Mesh Generation 5
4 Data Structures and Implementation Issues 8
5 Finite Volume Methods for Cut Cells 10
5.1 Steady-State Solution Techniques 12
5.2 Explicit Time-dependent Solution Techniques 13
5.3 Viscous Flows 17
6 Conclusions 18
Acknowledgements 18
References 18
2. Inverse Lax-Wendroff Procedure for Numerical
Boundary Treatment of Hyperbolic Equations 23
C.-l/V. Shu and S. Tan
1 Introduction 24
2 Problem Description and Interior Schemes 27
3 Numerical Boundary Conditions for Static Geometry 28
3.1 One-Dimensional Scalar Conservation Laws:
Smooth Solutions 28
3.2 One-Dimensional Scalar Conservation Laws:
Solutions Containing Discontinuities 31
3.3 Two-Dimensional Euler Equations in Static Geometry 34
4 Moving Boundary Treatment for Compressible
Inviscid Flows 38
5 Numerical Results 42
6 Conclusions and Future Work 48
References 49
3. Multidimensional Upwinding 53
R Roe
1 introduction 53
2 Why Multidimensional Methods? 57
2.1 Dimensional Splitting and One-Dimensional Upwinding 58
3 Oblique Wave Methods 61
4 Corner Transport Methods 62
5 Edges or Corners? 64
6 When Upwinding Is Not Needed 65
7 Bicharacteristic Methods 67
8 Residual Distribution 69
8.1 The N Scheme 70
8.2 The NN Scheme 71
8.3 Systems of Equations 72
8.4 Unsteady Problems 72
8.5 Wave Models 73
8.6 Elliptic-Hyperbolic Splitting 73
9 The Poisson Formulas 75
9.1 Application to the Euler Equations 76
10 Concluding Remarks 78
References 78
4. Bound-Preserving High-Order Schemes 81
Z. Xu and X. Zhang
1 Introduction 82
2 A Bound-Preserving Limiter for Approximation Polynomials 83
2.1 First-Order Monotone Schemes 83
2.2 The Weak Monotonicity in High-Order Finite
Volume Schemes 84
2.3 A Simple and Efficient Scaling Limiter 86
2.4 SSP High-Order Time Discretizations 91
2.5 Extensions and Applications 92
3 Bound-Preserving Flux Limiters 93
3.1 Basic Idea and Framework 93
3.2 Decoupling for the Flux Limiting Parameters 95
4 Concluding Remarks 97
Acknowledgements 98
References 98
5. Asymptotic-Preserving Schemes for Multiscale
Hyperbolic and Kinetic Equations 103
J. Hu, S. Jin, and Q. Li
1 Introduction 104
2 Basic Design Principles of AP Schemes—Two
Illustrative Examples 105
2.1 The Jin-Xin Relaxation Model 105
2.2 The BGK Model 107
3 AP Schemes for General Hyperbolic and Kinetic Equations 110
3.1 AP Schemes Based on Penalization 111
3.2 AP Schemes Based on Exponential Reformulation 115
3.3 AP Schemes Based on Micro-Macro Decomposition 117
4 Other Asymptotic Limits and AP Schemes 118
4.1 Diffusion Limit of Linear Transport Equation 118
4.2 High-Field Limit 119
4.3 Quasi-Neutral Limit in Plasmas 120
4.4 Low Mach Number Limit of Compressible Flows 121
4.5 Stochastic AP Schemes 122
5 Conclusion 123
Acknowledgements 123
References 124
6. Well-Balanced Schemes and Path-Conservative
Numerical Methods 131
M.J. Castro, I Morales de Luna, and C. Parés
1 Introduction 132
2 Path-Conservative Numerical Schemes 138
3 Some Families of Path-Conservative Numerical Schemes 142
3.1 Godunov Method 142
3.2 Simple Riemann Solvers 142
3.3 Roe Methods 144
3.4 Functional Viscosity Matrix Methods 145
3.5 Other Path-Conservative Methods 148
4 High-Order Schemes Based on Reconstruction of States 148
5 Well-Balanced Schemes 151
5.1 Well-Balanced Property for SRSs 154
5.2 Well-Balanced HLL Scheme 155
5.3 Well-Balanced SRSs 156
5.4 Roe Method 156
5.5 Well-Balanced Functional Viscosity Matrix Methods 157
5.6 Generalized Hydrostatic Reconstruction 158
5.7 Well-Balanced Methods for a Subset of Stationary
Solutions 160
5.8 High-Order Well-Balanced Schemes 161
6 Convergence and Choice of Paths 1 66
Acknowledgements 169
References 169
7. A Practical Guide to Deterministic Particle Methods 177
A. Chertock
1 Introduction 178
2 Description of the Particle Method 181
2.1 Particle Approximation of the Initial Data 182
2.2 Time Evolution of Particles 183
2.3 Particle Function Approximations 186
3 Remeshing for Particle Distortion 190
3.1 Particle Weights Redistribution 191
3.2 Particle Merger—A Local Redistribution Technique 193
4 Applications to Convection-Diffusion Equations 194
4.1 Particle Methods for Convection—Diffusion
Equations 195
Acknowledgements 198
References 198
8- On the Behaviour of Upwind Schemes
in the Low Mach Number Limit: A Review 203
H. Guiilard and B. Nkonga
1 Introduction 204
2 The Multiple Low Mach Number Limits of the
Compressible Euler Equations 205
2.1 Incompressible Limit 205
2.2 Acoustic Limit 207
2.3 Acoustic—Incompressible Interactions 208
2.4 Finite Volume Schemes 213
2.5 The Diagnosis 215
2.6 The Remedies 217
3 Numerical Illustrations 221
3.1 Order 1: Quadrangular Cartesian Grids 221
3.2 Order 1: Vertex-Centred Triangular Meshes 223
3.3 Order 1: Cell-Centred Triangular Meshes 224
3.4 Order 2: Vertex-Centred Triangular Meshes 226
« 4 Conclusion 228
References 228
9. Adjoint Error Estimation and Adaptivity
for Hyperbolic Problems 233
R Houston
1 Introduction 234
2 Error Representation for Linear Problems 235
2.1 Abstract Framework 236
2.2 Stabilized FEMs for the Linear Transport Equation 240
3 A Posteriori Error Estimation 243
4 Nonlinear Hyperbolic Conservation Laws 247
5 Practical Implementation and Adaptive Mesh Refinement 251
5.1 Numerical Approximation of the Dual Problem 251
5.2 Adaptive Mesh Refinement 252
5.3 Bibliographical Comments 253
6 Applications 254
6.1 Inviscid Flow Around a BAC3-11 Airfoil 254
6.2 Criticality Problems 255
6.3 Bifurcation Problems 255
7 Concluding Remarks and Outlook 256
Acknowledgements 258
References 258
10. Unstructured Mesh Generation and Adaptation 263
A. Loseille
1 Introduction 264
1.1 Outline 266
2 An Introduction to Unstructured Mesh Generation 266
2.1 Surface Mesh Generation 266
2.2 Volume Mesh Generation 267
3 Metric-Based Mesh Adaptation 269
3.1 Metric Tensors in Mesh Adaptation 271
3.2 Techniques for Enhancing Robustness and Performance 272
3.3 Metric-Based Error Estimates 274
3.4 Controlling the Interpolation Error 276
3.5 Geometric Estimate for Surfaces 277
3.6 Boundary Layers Metric 278
4 Algorithms for Generating Anisotropic Meshes 280
4.1 Insertion and Collapse 280
4.2 Optimizations and Enhancement for Unsteady
Simulations 282
5 Adaptive Algorithm and Numerical Illustrations 283
5.1 Adaptive Loop 284
5.2 A Wing-Body Configuration 285
5.3 Transonic Flow Around a M6 Wing 286
5.4 Direct Sonic Boom Simulation 288
5.5 Boundary Layer Shock Interaction 290
5.6 Double Mach Reflection and Blast Prediction 294
6 Conclusion 296
References 297
11. The Design of Steady State Schemes
for Computational Aerodynamics 303
ED. Witherden, A. Jameson, and D.W. Zingg
1 Introduction 304
2 Equations of Gas Dynamics and Spatial Discretizations 305
3 Time-Marching Methods 308
3.1 Model Problem for Stability Analysis
of Convection Dominated Problems 308
3.2 Multistage Schemes for Steady State Problems 309
3.3 Implicit Schemes for Steady State Problems 312
3.4 Acceleration Methods 318
3.5 Multigrid Methods 323
3.6 RANS Equations 327
4 Newton-Krylov Methods 332
4.1 Background 332
4.2 Methodology 335
5 Conclusions 344
References 345
12. Some Failures of Riemann Solvers 351
R. Abgrall
1 Introduction 351
2 Real Gas Effects 353
2.1 Mixture of Gases 353
2.2 Nonlinear Equation of State 355
3 Multidimensional Effects 356
4 Accuracy Effects 358
References 360
13. Numerical Methods for the Nonlinear
Shallow Water Equations 361
Y Xing
1 Overview 362
2 Mathematical Model 363
3 Numerical Methods 364
3.1 Numerical Methods for the Homogeneous Equations 364
3.2 Well-Balanced Methods 368
3.3 Positivity-Preserving Methods 374
4 Shallow Water-Related Models 377
4.1 Shallow Water Flows Through Channels
With Irregular Geometry 377
4.2 Shallow Water Equations on the Sphere 378
4.3 Two-Layer Shallow Water Equations 379
5 Conclusion Remarks 380
Acknowledgements 380
References 380
14. Maxwell and Magnetohydrodynamic Equations 385
C.-D. Munz and E. Sonnendrücker
1 Introduction 386
2 Maxwell s Equations 386
2.1 The Model 386
2.2 Generalised Maxwell s Equations: Correcting the Fields 387
2.3 Cartesian Grids: Finite Difference and Spectral
Methods 389
2.4 FV Schemes 390
2.5 Discontinuous Galerkin Schemes 393
2.6 Finite Element Methods 394
3 Magnetohydrodynamics 396
3.1 The Model 396
3.2 Discretization 397
4 Conclusion 398
References 398
15. Deterministic Solvers for Nonlinear Collisional
Kinetic Flows: A Conservative Spectral Scheme
for Boltzmann Type Flows 403
I.M. Gamba
1 introduction 404
1.1 Kinetic Evolution Models 404
1.2 Binary Collisional Models and Double Mixing
Convolution Forms 405
1.3 Classical Elastic Collisional Transport Theory:
The Boltzmann Equation 408
1.4 Deterministic Solvers for Integral Equations
of Boltzmann Type 409
2 The Landau and Boltzmann Operators Relation
Through Their Double Mixing Convolutional Forms 410
2.1 The Grazing Collision Limit 413
3 A Conservative Spectral Method for the Collisional Form 415
3.1 Choosing a Computational Cut-Off Domain QL 416
3.2 Fourier Series, Projections and Extensions 418
3.3 A Conservative Spectral Method for the
Homogeneous Boltzmann Equation 419
3.4 Conservation Method—An Extended Isoperimetric
Problem 421
3.5 Discrete in Time Conservation Method: Lagrange
Multiplier Method 425
4 Local Existence, Convergence and Regularity
for the Semidiscrete Scheme 426
4.1 Local Existence 427
4.2 Uniform Propagation of Numerical Unconserved Moments 428
4.3 Uniform /.£ Integrability Propagation 429
4.4 Uniform Semidiscrete /-/¿.Sobolev Regularity Propagation 430
5 Final Comments and Conclusions 431
Acknowledgements 432
References 432
16. Numerical Methods for Hyperbolic Nets
and Networks 435
v
S. Canic, M.L. Delle Monache, B. Piccoli, J.-M. Qiu,
and /. Tambaca
1 Introduction 436
2 Examples of Nets and Networks 437
2.1 Examples of Hyperbolic Nets 438
2.2 Examples of Hyperbolic Networks 446
3 Numerics for Nets and Networks 450
3.1 Finite Volume Methods 451
3.2 Discontinuous Galerkin Methods 451
References 460
17. Numerical Methods for Astrophysics 465
C. Klingenberg
1 Introduction 466
2 Astrophysical Scales for Astrophysical Phenomena 466
2.1 Spatial Scales 466
2.2 Density and Temporal Scales 466
3 Equations Used in Astrophysical Modelling 467
3.1 Source Terms 468
3.2 Additional Force Terms 468
3.3 Equation of State 469
4 Numerical Methods 469
4.1 Finite Difference Methods 469
4.2 Finite Volume Methods 470
4.3 Discontinuous Galerkin Method 471
4.4 N-Body Method 472
4.5 Grid-Free Method: Smoothed Particle
Hydrodynamics 472
5 High-Performance Computing 473
6 Astrophysical Codes 473
7 Conclusion 475
Acknowledgement 475
References 475
18. Numerical Methods for Conservation Laws
With Discontinuous Coefficients 479
S. Mishra
1 Introduction 480
1.1 Conservation Laws With Coefficients 481
2 Motivating Examples 481
2.1 Multiphase Flows in Porous Media 481
2.2 Traffic Flow 482
2.3 Other Examples of Scalar Conservation Laws With
Discontinuous Flux 483
2.4 Wave Propagation in Heterogeneous Media 484
2.5 Systems of Conservation Laws With Singular
Source Terms 484
2.6 Flows as Perturbations of Discontinuous
Steady States 485
3 A Brief Review of Available Theoretical Results 485
4 Numerical Schemes 491
4.1 Aligned Schemes 491
4.2 Staggered Schemes 493
4.3 Higher-Order Schemes 494
4.4 Extensions and Other Approaches 495
5 Numerical Experiments 496
5.1 Numerical Experiment 1 496
5.2 Numerical Experiment 2 497
5.3 Numerical Experiment 3 498
6 Summary and Open Problems 500
Acknowledgement 502
References 502
19. Uncertainty Quantification for Hyperbolic
Systems of Conservation Laws 507
R. Abgrall and S. Mishra
1 Introduction 508
1.1 Numerical Methods 509
1.2 Uncertainty Quantification 510
2 Random Fields and Random Entropy Solutions 511
2.1 Modelling of Random Inputs 512
2.2 Random Entropy Solutions 514
3 sC Method for UQ 515
3.1 Generalized Polynomial Chaos 516
3.2 Standard sG Method 517
3.3 gPC Expansions in the Entropy Variables 518
4 Stochastic Collocation Methods 520
4.1 Standard Stochastic Collocation Method 520
4.2 Stochastic Finite Volume Methods 521
5 Monte Carlo and Multilevel Monte Carlo Methods 524
5.1 Monte Carlo Method 524
5.2 Multilevel Monte Carlo Finite Volume Method 526
6 Numerical Experiments 529
6.1 Compressible Euler Equations 529
6.2 Uncertain Orszag—Tang Vortex 530
6.3 UQ for the Lituya Bay Mega-Tsunami 533
6.4 A Random Kelvin—Helmholtz Problem 534
7 Measure-Valued and Statistical Solutions 536
8 Conclusion and Perspectives 538
Acknowledgements 540
References 540
20. Multiscale Methods for Wave Problems in
Heterogeneous Media 545
A. Abdulle and R Henning
1 Introduction 546
2 Numerical Methods for the Wave Equation
in Heterogeneous Media Without Scale Separation 549
2.1 Approach 1—Harmonic Coordinate Transformations 551
2.2 Approach 2—MsFEM Using Limited Global Information 553
2.3 Approach 3—Flux-Transfer Transformations 555
2.4 Approach 4—Localized Orthogonal Decomposition 558
2.5 The Case of General Initial Values: G-Convergence
and Perturbation Arguments 561
3 Numerical Methods for the Wave Equation
in Heterogeneous Media With Scale Separation 563
3.1 Effective Model and Numerical Homogenization
Method for Short-Time Wave Propagation 564
3.2 Effective Model and Numerical Homogenization
Method for Long-Time Wave Propagation 569
Acknowledgement 574
References 574
Index 577
|
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| id | DE-604.BV044192331 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T17:56:29Z |
| institution | BVB |
| isbn | 9780444639103 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029599069 |
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| physical | xix, 589 Seiten Illustrationen, Diagramme (teilweise farbig) |
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| title | Handbook of numerical analysis |
| title_auth | Handbook of numerical analysis |
| title_exact_search | Handbook of numerical analysis |
| title_full | Handbook of numerical analysis Volume 18 Handbook of numerical methods for hyperbolic problems : applied and modern issues general editor: P. G. Ciarlet (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie), J. L. Lions |
| title_fullStr | Handbook of numerical analysis Volume 18 Handbook of numerical methods for hyperbolic problems : applied and modern issues general editor: P. G. Ciarlet (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie), J. L. Lions |
| title_full_unstemmed | Handbook of numerical analysis Volume 18 Handbook of numerical methods for hyperbolic problems : applied and modern issues general editor: P. G. Ciarlet (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie), J. L. Lions |
| title_short | Handbook of numerical analysis |
| title_sort | handbook of numerical analysis handbook of numerical methods for hyperbolic problems applied and modern issues |
| topic_facet | Aufsatzsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029599069&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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