Semi-Lagrangian Advection Methods and Their Applications in Geoscience provides a much-needed resource on semi-Lagrangian theory, methods, and applications. Covering a variety of applications, the book brings together developments of the semi-Lagrangian in one place and offers a comparison of semi-Lagrangian methods with Eulerian-based approaches. It also includes a chapter dedicated to difficulties of dealing with the adjoint of semi-Lagrangian methods and illustrates the behavior of different schemes for different applications. This allows for a better understanding of which schemes are most efficient, stable, consistent, and likely to introduce the minimum model error into a given problem.
Beneficial for students learning about numerical approximations to advection, researchers applying these techniques to geoscientific modeling, and practitioners looking for the best approach for modeling, Semi-Lagrangian Advection Methods and Their Applications in Geoscience fills a crucial gap in numerical modeling and data assimilation in geoscience.
1. Chapter 1: Introduction - p. iv 2. Chapter 2: Eulerian modeling of advection problems - p. 5 3. Chapter 3: Stability, consistency, and convergence of Eulerian advection based numerical methods - p. 67 4. Chapter 4: History of semi-Lagrangian methods - p. 108 5. Chapter 5: Semi-Lagrangian methods for linear advection problems - p. 127 6. Chapter 6: Interpolation methods - p. 146 7. Chapter 7: Stability and consistency analysis of semi-Lagrangian methods for the linear problem - p. 173 8. Chapter 8: Advection with nonconstant velocities - p. 203 9. Chapter 9: Nonzero forcings - p. 234 10. Chapter 10: Semi-Lagrangian methods for two-dimensional problems - p. 267 11. Chapter 11: Semi-Lagrangian methods for three-dimensional problems - p. 350 12. Chapter 12: Semi-Lagrangian methods on a sphere - p. 380 13. Chapter 13: Shape-preserving and mass-conserving semi-Lagrangian approaches - p. 469 14. Chapter 14: Tangent linear modeling and adjoints of semi-Lagrangian methods - p. 540 15. Chapter 15: Applications of semi-Lagrangian methods in the geosciences - p. 567 16. Chapter 16: Solutions to select exercises - p. 593 17. Bibliography - p. 597 18. Index - p. 605
Semi-Lagrangian Advection Methods and Their Applications in Geoscience provides a much-needed resource on semi-Lagrangian theory, methods, and applications. Covering a variety of applications, the book brings together developments of the semi-Lagrangian in one place and offers a comparison of semi-Lagrangian methods with Eulerian-based approaches. It also includes a chapter dedicated to difficulties of dealing with the adjoint of semi-Lagrangian methods and illustrates the behavior of different schemes for different applications. This allows for a better understanding of which schemes are most efficient, stable, consistent, and likely to introduce the minimum model error into a given problem.
Beneficial for students learning about numerical approximations to advection, researchers applying these techniques to geoscientific modeling, and practitioners looking for the best approach for modeling, Semi-Lagrangian Advection Methods and Their Applications in Geoscience fills a crucial gap in numerical modeling and data assimilation in geoscience.
1. Chapter 1: Introduction - p. iv 2. Chapter 2: Eulerian modeling of advection problems - p. 5 3. Chapter 3: Stability, consistency, and convergence of Eulerian advection based numerical methods - p. 67 4. Chapter 4: History of semi-Lagrangian methods - p. 108 5. Chapter 5: Semi-Lagrangian methods for linear advection problems - p. 127 6. Chapter 6: Interpolation methods - p. 146 7. Chapter 7: Stability and consistency analysis of semi-Lagrangian methods for the linear problem - p. 173 8. Chapter 8: Advection with nonconstant velocities - p. 203 9. Chapter 9: Nonzero forcings - p. 234 10. Chapter 10: Semi-Lagrangian methods for two-dimensional problems - p. 267 11. Chapter 11: Semi-Lagrangian methods for three-dimensional problems - p. 350 12. Chapter 12: Semi-Lagrangian methods on a sphere - p. 380 13. Chapter 13: Shape-preserving and mass-conserving semi-Lagrangian approaches - p. 469 14. Chapter 14: Tangent linear modeling and adjoints of semi-Lagrangian methods - p. 540 15. Chapter 15: Applications of semi-Lagrangian methods in the geosciences - p. 567 16. Chapter 16: Solutions to select exercises - p. 593 17. Bibliography - p. 597 18. Index - p. 605
