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Phase and Group Velocities of 2D Numerical Approximations for Hyperbolic Equations

Anton Antonov
Organization: Wolfram Research, Inc.
Department: Kernel Technology
URL: http://www.imm.dtu.dk/~uniaaa/

2004 International Mathematica Symposium
Conference location

Banff, Canada

Advection equations or modules containing the advection equation appear in many applications. It is shown in this paper that appropriate splitting techniques can be applied to divide large‐scale air pollution models into several simpler sub‐models. One of these sub‐models consists of only the advection equation. Several numerical methods for treatment of the advection equations are sketched. Then general definitions of some important quantities (first and foremost, the phase velocity and the group velocity) are given. Formulae for the phase velocity and the group velocity are derived for several methods for treatment of the advection equation arising in air pollution models. The major tool used in the derivation of these formulae is Mathematica. The results are plotted. The approach used here can be applied not only to advection equations arising in air pollution modeling, but also to those arising in other fluid dynamics problems.

*Applied Mathematics > Numerical Methods
*Mathematics > Calculus and Analysis > Differential Equations
*Science > Physics > Fluid Mechanics

Advection equation, splitting techniques, air pollution model, phase velocity, group velocity, fluid dynamics problems, hyperbolic equations
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