Computational Methods in Transport: Verification and Validation (eBook)

Preface 5
List of Contributors 7
Contents 9
Verification (Mostly) for High Energy Density Radiation Transport: Five Case Studies 11
1 Introduction 11
2 Case 1: The Marshak Wave 12
3 Case 2: Star-in-Space Problem 15
4 Case 3: The Radiating Shock Problem 18
5 Case 4: The Crooked Pipe 22
6 Case 5: Angle, Angles, Angles 23
7 Conclusion 25
Acknowledgments 26
References 26
A General Strategy for Physics-Based Model Validation Illustrated with Earthquake Phenomenology, Atmospheric Radiative Transfer, and Computational Fluid Dynamics 29
1 Introduction: Our Position with Respect to Previous Work on Validation and Related Concepts 29
2 Validation as a Constructive Iterative Process 42
3 Desirable Properties of the Multiplier of the Validation Step 48
4 Practical Guidelines for Determining p/q and cnovel 51
5 Illustration with the Development of Quantum Mechanics 53
6 Three Examples Drawn from the Authors’ Research Interests 55
7 Summary 63
Acknowledgments 64
Appendix: A More Formal Look at the Role of Validation in the Modeling Enterprise 64
References 76
Spectral Solvers to Non-Conservative Transport for Non- Linear Interactive Systems of Boltzmann Type 85
1 Introduction 85
2 The Non-Linear Boltzmann Equation for Binary Particle Interactions 87
3 Numerical Method and Discretization 97
4 Numerical Results 101
5 Conclusions and Future Work 111
Acknowledgments 111
References 112
The Art of Analytical Benchmarking 115
1 Introduction 115
2 The Theoretical Setting 117
3 The Numerical Setting 120
4 Mining the Discrete Ordinates Solution 126
5 Conclusions 139
References 144
Implicit Monte Carlo Radiation Transport Simulations of Four Test Problems 145
1 The Units Used for the Simulations Described in this Work 145
2 A Gray Infinite Medium Problem with a Matter Energy Source Allowing an Analytic Answer 146
3 A Cube with a Face Source Allowing an Approximate Analytic Answer 147
4 Graziani’s Spherical Multigroup Prompt Spectrum Test Problem 149
5 A Slab Version of Graziani’s Prompt Spectrum Test Problem 156
Acknowledgment 157
References 160
The Prompt Spectrum of a Radiating Sphere: Benchmark Solutions for Diffusion and Transport 161
1 Introduction 161
2 The Prompt Spectrum: Problem Definition 163
3 The Prompt Spectrum: Mathematical Derivation 164
Acknowledgments 176
References 176
Some Verification Problems with Possible Transport Applications 179
Introduction 179
1 Open Radiation Boundary Test 179
2 Spherical Heat Flow Test 181
3 Coupled Multi-Temperature Diffusion Test 183
4 Conclusion 184
Acknowledgment 185
References 185
Canopy Reflectance Model Benchmarking: RAMI and the ROMC 187
1 The Organisation of RAMI 188
2 The RAMI Protocol 195
3 The RAMI On-Line Model Checker 206
4 Conclusion 213
Acknowledgments 213
References 214
Uncertainty and Sensitivity Analysis for Models of Complex Systems 217
1 Introduction 217
2 Characterization of Uncertainty 218
3 Generation of Sample 219
4 Propagation of Sample Through the Analysis 222
5 Presentation of Uncertainty Analysis Results 223
6 Determination of Sensitivity Analysis Results 224
7 Summary 230
Acknowledgments 231
References 231
A Brief Overview of the State-of-the-Practice and Current Challenges of Solution Verification 239
1 Introduction 239
2 The Asymptotic Regime of Convergence 241
3 State-of-the-Practice to Verify the Convergence of Solutions 244
4 The Grid Convergence Index 249
5 Application of Solution Veri.cation to a Finite Element Calculation 251
6 Discussion of the Challenges of Code and Solution Verification 254
7 Conclusion 258
Acknowledgments 259
References 259
Expert Panel Opinion and Global Sensitivity Analysis for Composite Indicators 261
1 Introduction 261
2 Methodological Issues and Uncertainties in Building a Composite Indicator 264
3 Case Study: Technology Achievement Index and Expert Opinion 271
4 Results 275
5 Conclusions and Future Work 281
References 283
A Practical Global Sensitivity Analysis Methodology for Multi- Physics Applications 287
1 Introduction 287
2 A Global Sensitivity Analysis Methodology 288
3 Parameter Screening 291
4 Response Surface Analysis 298
5 Variance Decomposition 299
6 Validating our Sensitivity Analysis Methodology 304
7 PSUADE 306
8 Summary 307
Acknowledgment 308
References 308
Color Plates 311
Editorial Policy 337
General Remarks 338
Lecture Notes in Computational Science and Engineering 339
Monographs in Computational Science and Engineering 341
Texts in Computational Science and Engineering 342