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Comparison of numerical schemes for solving the advection equation

✍ Scribed by D. Bouche; G. Bonnaud; D. Ramos

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
403 KB
Volume
16
Category
Article
ISSN
0893-9659

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✦ Synopsis

Communicated by C. Bardos

Abstract--We report on the dispersion and dissipation properties of numerical schemes aimed at solving the one-dimensional advection equation. The study is based on the consistency error, which is explicitly calculated for various standard finite-difference schemes. The oscillation and damping features of the numerical solutions are shown to be explained via a generalized Airy-like function.

In the specific case of the advection of a step function, the solutions of the equivalent equations are systematically calculated and shown to recover the numerical solutions. A particular emphasis is put on one third-order accurate scheme, which involves a weak smearing of the step.

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