Multiple Time Scales

¿ContributorsPreface1. 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 References2. 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 References3. 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 References4. 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 References5. 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 References6. 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 References7. Multiple Time-Scale Methods in Tokamak Magnetohydrodynamics I. Introduction II. Ideal Time-Scale MHD Simulations III. Resistive Time-Scale MHD Simulations IV. Discussion References8. Hybrid and Collisional Implicit Plasma Simulation Models I. Introduction II. Basic Moment Method III. Collisional-Hybrid Extensions IV. Applications V. Conclusion References9. 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 References10. Orbit Averaging and Subcycling in Particle Simulation of Plasmas I. Introduction II. Electron Subcycling III. Orbit Averaging IV. Discussion References11. Direct Implicit Plasma Simulation I. Introduction II. Direct Method with Electrostatic Fields III. Gyroaveraged Particle Simulation IV. Electromagnetic Direct Implicit Method V. Concluding Remarks References12. 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 References13. 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 ReferencesSubject Index