http://home.eps.hw.ac.uk/~ab226/tmp/implicit/lele_92.pdf

Compact finite difference schemes with spectral-like resolution

This comprehensive text and reference work on numerical weather prediction, first published in 2002, covers not only methods for numerical modeling, but also the important related areas of data assimilation and predictability. It incorporates all aspects of environmental computer modeling including an historical overview of the subject, equations of motion and their approximations, a modern and clear description of numerical methods, and the determination of initial conditions using weather observations (an important science known as data assimilation). Finally, this book provides a clear discussion of the problems of predictability and chaos in dynamical systems and how they can be applied to atmospheric and oceanic systems. Professors and students in meteorology, atmospheric science, oceanography, hydrology and environmental science will find much to interest them in this book, which can also form the basis of one or more graduate-level courses.

/pdf/atmospheric-modeling-data-assimilation-and-predictability-1qxqadvqdq.pdf

Atmospheric Modeling, Data Assimilation and Predictability

Statistical physics of vehicular traffic and some related systems

(2005). Atmospheric Modeling, Data Assimilation, and Predictability. Technometrics: Vol. 47, No. 4, pp. 521-521.

Atmospheric Modeling, Data Assimilation, and Predictability

Wave propagation and group velocity

Mathematics and Computers in Simulation

Wave propagation and reflection in irregular grids for hyperbolic equations

There are spurious phenomena in the numerical approximation of the hyperbolic equations of fluid dynamics that may be investigated by invoking concepts which originate from wave propagation theory. Many of the significant results which have been obtained by pursuing this kind of analysis are reviewed in this paper by using as an illustration a family of implicit approximations of the simple linear advection equation. Included in this family of algorithms are the common six-point implicit finite difference scheme, the linear finite element/Galerkin scheme and the ‘box’ method.

The phase and group velocities of sinusoidal solutions are brought into the analysis of the accuracy and of the spurious reflection or scattering phenomena which are created at computational boundaries and in non-uniform grids. General properties become apparent in this Fourier/wave propagation approach to the analysis. One of these is in the form of an analogy with quantum mechanics. Another shows that certain energy norms of the errors are independent of time discretization, i.e. depend on space discretization alone.

Robert Vichnevetsky

Papers

Mathematics and Computers in Simulation

Wave propagation and reflection in irregular grids for hyperbolic equations

Wave propagation analysis of difference schemes for hyperbolic equations: A review

Propagation through numerical mesh refinement for hyperbolic equations

International Association for Mathematics and Computers in Simulation