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A comparison of the GWCE and mixed PNC1 – P1 formulations in finite-element linearized shallow-water models
Le Roux, D.Y.; Walters, R.; Hanert, E.; Pietrzak, J. (2012). A comparison of the GWCE and mixed PNC1 – P1 formulations in finite-element linearized shallow-water models. Int. J. Numer. Methods Fluids 68(12): 1497-1523. dx.doi.org/10.1002/fld.2540
In: International Journal for Numerical Methods in Fluids. Wiley Interscience: Chichester; New York. ISSN 0271-2091; e-ISSN 1097-0363
Peer reviewed article  

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Author keywords
    shallow-water equations; generalized wave continuity equation; finiteelements; dispersion analysis; gravity waves

Auteurs  Top 
  • Le Roux, D.Y.
  • Walters, R.
  • Hanert, E.
  • Pietrzak, J.

Abstract
    The appearance of spurious pressure modes in early shallow-water (SW) models has resulted in two common strategies in the finite element (FE) community: using mixed primitive variable and generalized wave continuity equation (GWCE) formulations of the SW equations. One FE scheme in particular, the P1NC - P1 pair, combined with the primitive equations may be advantageously compared with the wave equation formulations and both schemes have similar data structures. Our focus here is on comparing these two approaches for a number of measures including stability, accuracy, efficiency, conservation properties, and consistency. The main part of the analysis centres on stability and accuracy results via Fourier-based dispersion analyses in the context of the linear SW equations. The numerical solutions of test problems are found to be in good agreement with the analytical results.

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