Multiple Time Scales

1st Edition - August 1, 1985
Editors: Jeremiah U. Brackbill, Bruce I. Cohen
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 2 - 5 7 5 6 - 3

Multiple Time Scales presents various numerical methods for solving multiple-time-scale problems. The selection first elaborates on considerations on solving problems with… Read more

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Multiple Time Scales presents various numerical methods for solving multiple-time-scale problems. The selection first elaborates on considerations on solving problems with multiple scales; problems with different time scales; and nonlinear normal-mode initialization of numerical weather prediction models. Discussions focus on analysis of observations, nonlinear analysis, systems of ordinary differential equations, and numerical methods for problems with multiple scales. The text then examines the diffusion-synthetic acceleration of transport iterations, with application to a radiation hydrodynamics problem and implicit methods in combustion and chemical kinetics modeling. The publication ponders on molecular dynamics and Monte Carlo simulations of rare events; direct implicit plasma simulation; orbit averaging and subcycling in particle simulation of plasmas; and hybrid and collisional implicit plasma simulation models. Topics include basic moment method, electron subcycling, gyroaveraged particle simulation, and the electromagnetic direct implicit method. The selection is a valuable reference for researchers interested in pursuing further research on the use of numerical methods in solving multiple-time-scale problems.

Contributors

Preface

1. Considerations on Solving Problems with Multiple Scales

I. Introduction

II. Examples of Problems with Multiple Scales

III. Numerical Methods for Multiple-Scale Problems

IV. Summary and Perspectives

References

2. Problems with Different Time Scales

I. Introduction

II. Systems of Ordinary Differential Equations

III. Numerical Methods for Ordinary Differential Equations

IV. Partial Differential Equations

V. Shallow Water Equations

VI. Atmospheric Motions

VII. Plasma Physics

References

3. Nonlinear Normal-Mode Initialization of Numerical Weather Prediction Models

I. Introduction

II. Normal-Mode Analysis

III. Nonlinear Analysis

IV. Analysis of Observations

V. Remaining Problems

References

4. The Diffusion-Synthetic Acceleration of Transport Iterations, with Application to a Radiation Hydrodynamics Problem

I. Introduction

II. Transport Iteration Methods

III. A Problem in Radiation Hydrodynamics

IV. Time-Dependent Example Calculations

References

5. Implicit Methods in Combustion and Chemical Kinetics Modeling

I. Introduction

II. Stiffness and Implicit Methods

III. The Method of Lines

IV. Adaptive Meshing

V. Solution of the Nonlinear Equations

References

6. Implicit Adaptive-Grid Radiation Hydrodynamics

I. Introduction

II. Physical Equations

III. Adaptive-Mesh Equations

IV. Numerical Equations

V. The Adaptive Mesh

VI. Numerical Techniques

VII. Ordinary Gas Dynamics: Shock Tubes

VIII. Radiation Hydrodynamics: A Supercritical Shock

IX. A "Hubert Program" for Nonlinear Radiation Hydrodynamics

References

7. Multiple Time-Scale Methods in Tokamak Magnetohydrodynamics

I. Introduction

II. Ideal Time-Scale MHD Simulations

III. Resistive Time-Scale MHD Simulations

IV. Discussion

References

8. Hybrid and Collisional Implicit Plasma Simulation Models

I. Introduction

II. Basic Moment Method

III. Collisional-Hybrid Extensions

IV. Applications

V. Conclusion

References

9. Simulation of Low-Frequency Electromagnetic Phenomena in Plasmas

I. Introduction

II. Implicit Plasma Simulation

III. Implicit Formulation of the Dynamic Equations

IV. The Algorithm for the Implicit Moment Method

V. Properties of the Implicit Moment Method

VI. Computational Examples

VII. Conclusions

References

10. Orbit Averaging and Subcycling in Particle Simulation of Plasmas

I. Introduction

II. Electron Subcycling

III. Orbit Averaging

IV. Discussion

References

11. Direct Implicit Plasma Simulation

I. Introduction

II. Direct Method with Electrostatic Fields

III. Gyroaveraged Particle Simulation

IV. Electromagnetic Direct Implicit Method

V. Concluding Remarks

References

12. Direct Methods for N-Body Simulations

I. Introduction

II. Basic Formulation

III. Ahmad-Cohen Scheme

IV. Comoving Coordinates

V. Planetary Perturbations and Collisions

VI. Two-Body Regularization

VII. Three-Body Regularization

VIII. Star-Cluster Simulations

References

13. Molecular Dynamics and Monte Carlo Simulation of Rare Events

I. Introduction

II. Activated Barrier Crossing Theory and Methodology

III. Some Methods for Accelerating Simulations

IV. Summary

References

Subject Index