Griebel / Roose / Schlick Computational Methods in Transport: Verification and Validation

1. Auflage 2008
ISBN: 978-3-540-77362-7
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 332 Seiten

The focus of this book deals with a cross cutting issue affecting all transport disciplines, whether it be photon, neutron, charged particle or neutrino transport. That is, verification and validation. In this book, we learn what the astrophysicist, atmospheric scientist, mathematician or nuclear engineer do to assess the accuracy of their code. What convergence studies, what error analysis, what problems do each field use to ascertain the accuracy of their transport simulations.

Autoren/Hrsg.

Griebel, Michael

Roose, Dirk

Schlick, Tamar

Fra,

Graziani, Frank

Inhaltsverzeichnis

1;Preface;5
2;List of Contributors;7
3;Contents;9
4;Verification (Mostly) for High Energy Density Radiation Transport: Five Case Studies;11
4.1;1 Introduction;11
4.2;2 Case 1: The Marshak Wave;12
4.3;3 Case 2: Star-in-Space Problem;15
4.4;4 Case 3: The Radiating Shock Problem;18
4.5;5 Case 4: The Crooked Pipe;22
4.6;6 Case 5: Angle, Angles, Angles;23
4.7;7 Conclusion;25
4.8;Acknowledgments;26
4.9;References;26
5;A General Strategy for Physics-Based Model Validation Illustrated with Earthquake Phenomenology, Atmospheric Radiative Transfer, and Computational Fluid Dynamics;29
5.1;1 Introduction: Our Position with Respect to Previous Work on Validation and Related Concepts;29
5.2;2 Validation as a Constructive Iterative Process;42
5.3;3 Desirable Properties of the Multiplier of the Validation Step;48
5.4;4 Practical Guidelines for Determining p/q and cnovel;51
5.5;5 Illustration with the Development of Quantum Mechanics;53
5.6;6 Three Examples Drawn from the Authors’ Research Interests;55
5.7;7 Summary;63
5.8;Acknowledgments;64
5.9;Appendix: A More Formal Look at the Role of Validation in the Modeling Enterprise;64
5.10;References;76
6;Spectral Solvers to Non-Conservative Transport for Non- Linear Interactive Systems of Boltzmann Type;85
6.1;1 Introduction;85
6.2;2 The Non-Linear Boltzmann Equation for Binary Particle Interactions;87
6.3;3 Numerical Method and Discretization;97
6.4;4 Numerical Results;101
6.5;5 Conclusions and Future Work;111
6.6;Acknowledgments;111
6.7;References;112
7;The Art of Analytical Benchmarking;115
7.1;1 Introduction;115
7.2;2 The Theoretical Setting;117
7.3;3 The Numerical Setting;120
7.4;4 Mining the Discrete Ordinates Solution;126
7.5;5 Conclusions;139
7.6;References;144
8;Implicit Monte Carlo Radiation Transport Simulations of Four Test Problems;145
8.1;1 The Units Used for the Simulations Described in this Work;145
8.2;2 A Gray Infinite Medium Problem with a Matter Energy Source Allowing an Analytic Answer;146
8.3;3 A Cube with a Face Source Allowing an Approximate Analytic Answer;147
8.4;4 Graziani’s Spherical Multigroup Prompt Spectrum Test Problem;149
8.5;5 A Slab Version of Graziani’s Prompt Spectrum Test Problem;156
8.6;Acknowledgment;157
8.7;References;160
9;The Prompt Spectrum of a Radiating Sphere: Benchmark Solutions for Diffusion and Transport;161
9.1;1 Introduction;161
9.2;2 The Prompt Spectrum: Problem Definition;163
9.3;3 The Prompt Spectrum: Mathematical Derivation;164
9.4;Acknowledgments;176
9.5;References;176
10;Some Verification Problems with Possible Transport Applications;179
10.1;Introduction;179
10.2;1 Open Radiation Boundary Test;179
10.3;2 Spherical Heat Flow Test;181
10.4;3 Coupled Multi-Temperature Diffusion Test;183
10.5;4 Conclusion;184
10.6;Acknowledgment;185
10.7;References;185
11;Canopy Reflectance Model Benchmarking: RAMI and the ROMC;187
11.1;1 The Organisation of RAMI;188
11.2;2 The RAMI Protocol;195
11.3;3 The RAMI On-Line Model Checker;206
11.4;4 Conclusion;213
11.5;Acknowledgments;213
11.6;References;214
12;Uncertainty and Sensitivity Analysis for Models of Complex Systems;217
12.1;1 Introduction;217
12.2;2 Characterization of Uncertainty;218
12.3;3 Generation of Sample;219
12.4;4 Propagation of Sample Through the Analysis;222
12.5;5 Presentation of Uncertainty Analysis Results;223
12.6;6 Determination of Sensitivity Analysis Results;224
12.7;7 Summary;230
12.8;Acknowledgments;231
12.9;References;231
13;A Brief Overview of the State-of-the-Practice and Current Challenges of Solution Verification;239
13.1;1 Introduction;239
13.2;2 The Asymptotic Regime of Convergence;241
13.3;3 State-of-the-Practice to Verify the Convergence of Solutions;244
13.4;4 The Grid Convergence Index;249
13.5;5 Application of Solution Veri.cation to a Finite Element Calculation;251
13.6;6 Discussion of the Challenges of Code and Solution Verification;254
13.7;7 Conclusion;258
13.8;Acknowledgments;259
13.9;References;259
14;Expert Panel Opinion and Global Sensitivity Analysis for Composite Indicators;261
14.1;1 Introduction;261
14.2;2 Methodological Issues and Uncertainties in Building a Composite Indicator;264
14.3;3 Case Study: Technology Achievement Index and Expert Opinion;271
14.4;4 Results;275
14.5;5 Conclusions and Future Work;281
14.6;References;283
15;A Practical Global Sensitivity Analysis Methodology for Multi- Physics Applications;287
15.1;1 Introduction;287
15.2;2 A Global Sensitivity Analysis Methodology;288
15.3;3 Parameter Screening;291
15.4;4 Response Surface Analysis;298
15.5;5 Variance Decomposition;299
15.6;6 Validating our Sensitivity Analysis Methodology;304
15.7;7 PSUADE;306
15.8;8 Summary;307
15.9;Acknowledgment;308
15.10;References;308
16;Color Plates;311
17;Editorial Policy;337
18;General Remarks;338
19;Lecture Notes in Computational Science and Engineering;339
20;Monographs in Computational Science and Engineering;341
21;Texts in Computational Science and Engineering;342