Semi-Lagrangian Advection Methods and Their Applications in Geoscience

Semi-Lagrangian Advection Methods and Their Applications in Geoscience provides a much-needed resource on semi-Lagrangian theory, methods, and application. 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 behaviour of different schemes for different applications. This allows for a bitter 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

Students and researchers in geophysics, geochemistry, volcanology, atmospheric science, applied math, oceanography, and hydrology; Secondary audience in geophysical industry

1. Introduction to Advection/Transport Problems
   2. History of Semi-Lagrangian methods
   3. Eulerian Modelling of Advection/Transport
   4. Stability and Consistency of Eulerian Methods
   5. Semi-Lagrangian for constant linear Advection/Transport
   6. Interpolation Methods
   7. Non-constant velocity methods
   8. Non-zero/non-Linear Forcing
   9. Semi-Implicit Semi-Lagrangian Methods
   10. 2D modelling
   11. 3D Modelling
   12. Semi-Lagrangian methods on the sphere
   13. Adjoints of Eulerian and Semi-Lagrangian methods
   14. Applications in the geosciences.