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 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

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

1. Introduction
2. Eulerian modeling of advection problems
3. Stability, consistency, and convergence of Eulerian advection based numerical methods
4. History of semi-Lagrangian methods
5. Semi-Lagrangian methods for linear advection problems
6. Interpolation methods
7. Stability and consistency analysis of semi-Lagrangian methods for the linear problem
8. Advection with nonconstant velocities
9. Nonzero forcings
10. Semi-Lagrangian methods for two-dimensional problems
11. Semi-Lagrangian methods for three-dimentional problems
12. Semi-Lagrangian methods on a sphere
13. Shape-preserving and mass-conserving semi-Lagrangian approaches
14. Tangent linear modeling and adjoints of semi-Lagrangian methods
15. Applications of semi-Lagrangian methods in the geosciences