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.
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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
