Transport: Non-diffusive, flux conservative initial value problems and ...
Transport: Non-diffusive, flux conservative initial value problems and ...
Transport: Non-diffusive, flux conservative initial value problems and ...
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<strong>Transport</strong> equations 83<br />
they are more faithful to the underlying characteristics than Eulerian schemes, <strong>and</strong><br />
the lack of a courant condition makes them highly attractive for high-resolution<br />
<strong>problems</strong>. If you just need to get going though, a second order staggered leapfrog<br />
is the simplest first approach to try. If the numerical dispersion becomes annoying<br />
a more expensive mpdata scheme might be used but they are really superseded by<br />
the SL schemes. In all cases beware of simple upwind differences if numerical<br />
diffusion is not desired.<br />
Bibliography<br />
[1] B. P. Leonard. A survey of finite differences of opinion on numerical muddling<br />
of the incomprehensible defective confusion equation, in: T. J. R. Hughes, ed.,<br />
Finite element methods for convection dominated flows, vol. 34, pp. 1–17,<br />
Amer. Soc. Mech. Engrs. (ASME), 1979.<br />
[2] P. K. Smolarkiewicz. A simple positive definite advection scheme with small<br />
implicit diffusion, Mon Weather Rev 111, 479–486, 1983.<br />
[3] A. Staniforth <strong>and</strong> J. Cote. Semi-Lagrangian integration schemes for atmospheric<br />
models—A review, Mont. Weather Rev. 119, 2206–2223, Sep 1991.<br />
[4] W. H. Press, B. P. Flannery, S. A. Teukolsky <strong>and</strong> W. T. Vetterling. Numerical<br />
Recipes, Cambridge Univ. Press, New York, 2nd edn., 1992.