Description
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.- Provides a single resource for understanding semi-Lagrangian methods and what is involved in its application- Includes exercises and codes to supplement learning and create opportunities for practice- Includes coverage of adjoints, examining the advantages and disadvantages of different approaches in multiple coordinate systems and different discretizations- Includes links to numerical datasets and animations to further enhance understanding
Table of Contents
1. Introduction2. Eulerian modeling of advection problems3. Stability, consistency, and convergence of Eulerian advection based numerical methods4. History of semi-Lagrangian methods5. Semi-Lagrangian methods for linear advection problems6. Interpolation methods7. Stability and consistency analysis of semi-Lagrangian methods for the linear problem8. Advection with nonconstant velocities9. Nonzero forcings10. Semi-Lagrangian methods for two-dimensional problems11. Semi-Lagrangian methods for three-dimentional problems12. Semi-Lagrangian methods on a sphere13. Shape-preserving and mass-conserving semi-Lagrangian approaches14. Tangent linear modeling and adjoints of semi-Lagrangian methods15. Applications of semi-Lagrangian methods in the geosciences
