Numerical methods for wave equations in geophysical fluid dynamics / Численные методы решения волновых уравнений в геофизической гидродинамике

This book is designed to serve as a textbook for graduate students or advanced undergraduates studying numerical methods for the solution of partial differential equations goveming wave-like flows. Although the majority of the schemes presented in this text were introduced in either the applied-rnathematics or atmospheric- science literature, the focus is not on the nuts-and-bolts details of various atmospheric models but on fundamental numerical methods that have applications in a wide range of scientific and engineering disciplines. The prototype problems considered include tracer transport, shallow-water flow and the evolution of internal waves in a continuously stratified fluid.

A significant fraction of the literature on numerical methods for these problems falls into one of two categories, those books and papers that emphasize theorems and proofs , and those that emphasize numerical experimentation. Given the uncertainty associated with the messy compromises actually required to construct numerical approximations to real-world fluid-dynamics problems, it is difficult to emphasize theorems and proofs without limiting the analysis to classical numerical schemes whose practical application may be rather limited . On the other hand, if one relies primarilyon numerical experimentation it is much harder to arrive at conclusions that extend beyond a specific set of test cases. In an attempt to establish a clear link between theory and practice, I have tried to follow amiddie course between the theorern-and-proof formalism and the reliance on numerical experimentation. There are no formal proofs in this book , but the mathematical properties of each method are derived in a style familiar to physical scientists. At the same time, numerical examples are includcd that illustrate these theoretically derived properties and facilitate the intercomparison of various methods . <...>