Multiple Time Scales - 1st Edition - ISBN: 9780121234201, 9781483257563

Multiple Time Scales

1st Edition

Editors: Jeremiah U. Brackbill Bruce I. Cohen
eBook ISBN: 9781483257563
Imprint: Academic Press
Published Date: 1st August 1985
Page Count: 456
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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.

Table of Contents



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


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


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


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


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


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


7. Multiple Time-Scale Methods in Tokamak Magnetohydrodynamics

I. Introduction

II. Ideal Time-Scale MHD Simulations

III. Resistive Time-Scale MHD Simulations

IV. Discussion


8. Hybrid and Collisional Implicit Plasma Simulation Models

I. Introduction

II. Basic Moment Method

III. Collisional-Hybrid Extensions

IV. Applications

V. Conclusion


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


10. Orbit Averaging and Subcycling in Particle Simulation of Plasmas

I. Introduction

II. Electron Subcycling

III. Orbit Averaging

IV. Discussion


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


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


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


Subject Index


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© Academic Press 1985
Academic Press
eBook ISBN:

About the Editor

Jeremiah U. Brackbill

Bruce I. Cohen

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