TY - JOUR
T1 - On the Inaccuracies of Some Finite Volume Discretizations of the Linearized Shallow Water Problem
AU - S. Faure, M. Petcu, R. Temam & J. Tribbia
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 518
EP - 541
PY - 2011
DA - 2011/08
SN - 8
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/699.html
KW - finite volume discretizations, spurious caustics, numerical error, dispersion relation, hyperbolic systems.
AB - <p style="text-align: justify;">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.</p>