Front Cover 1
Multiple Time Scales 4
Copyright Page 5
Table of Contents 6
Contributors 10
Preface 12
Chapter 1. Considerations on Solving Problems with Multiple Scales 16
I. INTRODUCTION 16
II. EXAMPLES OF PROBLEMS WITH MULTIPLE SCALES 18
III. NUMERICAL METHODS FOR PROBLEMS WITH MULTIPLE SCALES 26
IV. SUMMARY AND PERSPECTIVES 38
ACKNOWLEDGMENT 39
REFERENCES 39
Chapter 2. Problems with Different Time Scales 44
I. INTRODUCTION 44
II. SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS 47
III. NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS 51
IV. PARTIAL DIFFERENTIAL EQUATIONS 55
V. SHALLOW WATER EQUATIONS 59
VI. ATMOSPHERIC MOTIONS 64
VII. PLASMA PHYSICS 70
REFERENCES 71
Chapter 3. Nonlinear Normal-Mode Initialization of Numerical Weather Prediction Models 74
I. INTRODUCTION 74
II. NORMAL-MODE ANALYSIS 77
III. NONLINEAR ANALYSIS 80
IV. ANALYSIS OF OBSERVATIONS 83
V. REMAINING PROBLEMS 85
REFERENCES 86
Chapter 4. The Diffusion-Synthetic Accelerationof Transport Iterations,with Application to a Radiation Hydrodynamics Problem 88
I. INTRODUCTION 89
II. TRANSPORT ITERATION METHODS 90
III. A PROBLEM IN RADIATION HYDRODYNAMICS 99
IV. TIME-DEPENDENT EXAMPLE CALCULATIONS 119
REFERENCES 126
Chapter 5. Implicit Methods in Combustionand Chemical Kinetics Modeling 128
I. INTRODUCTION 128
II. STIFFNESS AND IMPLICIT METHODS 130
III. THE METHOD OF LINES 137
IV. ADAPTIVE MESHING 142
V. SOLUTION OF THE NONLINEAR EQUATIONS 153
REFERENCES 157
Chapter 6. Implicit Adaptive-Grid Radiation Hydrodynamics 160
I. INTRODUCTION 161
II. PHYSICAL EQUATIONS 163
III. ADAPTIVE-MESH EQUATIONS 168
IV. NUMERICAL EQUATIONS 170
V. THE ADAPTIVE MESH 172
VI. NUMERICAL TECHNIQUES 175
VII. ORDINARY GAS DYNAMICS: SHOCK TUBES 184
VIII. RADIATION HYDRODYNAMICS:A SUPERCRITICAL SHOCK 188
IX. A "HILBERT PROGRAM" FOR NONLINEAR RADIATION HYDRODYNAMICS 194
REFERENCES 198
Chapter 7. Multiple Time-Scale Methods in Tokamak Magnetohydrodynamics 200
I. INTRODUCTION 201
II. IDEAL TIME-SCALE MHD SIMULATIONS 208
III. RESISTIVE TIME-SCALE MHD SIMULATIONS 224
IV. DISCUSSION 244
ACKNOWLEDGMENTS 246
REFERENCES 246
Chapter 8. Hybrid and Collisional Implicit Plasma Simulation Models 248
I. INTRODUCTION 248
II. BASIC MOMENT METHOD 251
III. COLLISIONAL-HYBRID EXTENSIONS 264
IV. APPLICATIONS 279
V. CONCLUSION 282
ACKNOWLEDGMENTS 284
REFERENCES 284
Chapter 9. Simulation of Low-Frequency,Electromagnetic Phenomenain Plasmas 286
I. INTRODUCTION 287
II. IMPLICIT PLASMA SIMULATION 289
III. IMPLICIT FORMULATION OF THE DYNAMIC EQUATIONS 295
IV. THE ALGORITHM FOR THE IMPLICIT MOMENT METHOD 308
V. PROPERTIES OF THE IMPLICIT MOMENT METHOD 310
VI. COMPUTATIONAL EXAMPLES 315
VII. CONCLUSIONS 323
ACKNOWLEDGMENTS 324
REFERENCES 324
Chapter 10. Orbit Averaging and Subcycling in Particle Simulation of Plasmas 326
I. INTRODUCTION 326
II. ELECTRON SUBCYCLING 331
III. ORBIT AVERAGING 335
IV. DISCUSSION 344
ACKNOWLEDGMENTS 347
REFERENCES 347
Chapter 11. Direct Implicit Plasma Simulation 350
I. INTRODUCTION 351
II. DIRECT METHOD WITH ELECTROSTATIC FIELDS 356
III. GYROAVERAGED PARTICLE SIMULATION 376
IV. ELECTROMAGNETIC DIRECT IMPLICIT METHOD 381
V. CONCLUDING REMARKS 388
ACKNOWLEDGMENTS 389
REFERENCES 389
Chapter 12. Direct Methods for N-Body Simulations 392
I. INTRODUCTION 393
II. BASIC FORMULATION 396
III. AHMAD–COHEN SCHEME 400
IV. COMOVING COORDINATES 404
V. PLANETARY PERTURBATIONS AND COLLISIONS 409
VI. TWO-BODY REGULARIZATION 413
VII. THREE-BODY REGULARIZATION 424
VIII. STAR-CLUSTER SIMULATIONS 428
ACKNOWLEDGMENTS 432
REFERENCES 432
Chapter 13. Molecular Dynamics and Monte Carlo Simulations of Rare Events 434
I. INTRODUCTION 434
II. ACTIVATED BARRIER CROSSING:THEORY AND METHODOLOGY 436
III. SOME METHODS FOR ACCELERATING SIMULATIONS 445
IV. SUMMARY 450
REFERENCES 450
Index 452