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Volume 8, Issue 3
On the Inaccuracies of Some Finite Volume Discretizations of the Linearized Shallow Water Problem

S. Faure, M. Petcu, R. Temam & J. Tribbia

Int. J. Numer. Anal. Mod., 8 (2011), pp. 518-541.

Published online: 2011-08

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  • 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.

  • Keywords

finite volume discretizations, spurious caustics, numerical error, dispersion relation, hyperbolic systems.

  • AMS Subject Headings

35L60, 35Q35, 76B15, 76B65

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-8-518, author = {S. Faure, M. Petcu, R. Temam and J. Tribbia}, title = {On the Inaccuracies of Some Finite Volume Discretizations of the Linearized Shallow Water Problem}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2011}, volume = {8}, number = {3}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/699.html} }
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 -

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.

S. Faure, M. Petcu, R. Temam and J. Tribbia. (2011). On the Inaccuracies of Some Finite Volume Discretizations of the Linearized Shallow Water Problem. International Journal of Numerical Analysis and Modeling. 8 (3). 518-541. doi:
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