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Comparison of several numerical schemes applied to advection equations

✍ Scribed by Zbyněk Sokol

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
753 KB
Volume
125
Category
Article
ISSN
0035-9009

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✦ Synopsis

Abstract

Eight numerical‐solution methods of advection equations are compared using two tests: the rotational flowfield test and the deformational flow‐field test. Beside the leap‐frog difference scheme used as a reference method, all the other methods are positive definite or monotonicity preserving. the positive definiteness is either the property of the advection scheme or it is obtained by applying the flux transport limiter. the following schemes are studied: the leap‐frog scheme completed by a flux transport limiter, Bott's scheme, the piecewise parabolic method, one version of the total variation diminishing (TVD) scheme and three modifications of essentially non‐oscillatory (ENO) schemes. the aim is to compare the schemes with respect to the application of TVD and ENO schemes in atmospheric modelling with high resolution. the test results confirm that at least one of the ENO schemes tested may be applied, but apparently the best results are obtained by Bott's scheme.

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