Year: 2011
International Journal of Numerical Analysis and Modeling, Vol. 8 (2011), Iss. 3 : pp. 518–541
Abstract
In this article we are interested in the study of the errors introduced by different finite volume discretizations in the study of the wave frequencies. This study is made in the context of hyperbolic systems arising in meteorology and oceanography. We show the existence of significant errors in the dispersion relation, only the long waves being computed accurately; this conclusion is similar to the finite differences case described in the article of Grotjahn and O’Brien quoted below. For the case of inertia-gravity waves, we study three often used schemes which are based on the upwind, centered or Lax-Wendroff fluxes. Moreover, the Total Variation Diminishing method (TVD) made from these fluxes (which usually provides an efficient way to eliminate spurious numerical oscillations) will give the same errors in the dispersion relation.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2011-IJNAM-699
International Journal of Numerical Analysis and Modeling, Vol. 8 (2011), Iss. 3 : pp. 518–541
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: finite volume discretizations spurious caustics numerical error dispersion relation hyperbolic systems.