Premium
A comparison of the GWCE and mixed P − P 1 formulations in finite‐element linearized shallow‐water models
Author(s) -
Roux D. Y. Le,
Walters R.,
Hanert E.,
Pietrzak J.
Publication year - 2011
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2540
Subject(s) - spurious relationship , mathematics , finite element method , shallow water equations , context (archaeology) , stability (learning theory) , consistency (knowledge bases) , mathematical analysis , fourier transform , geometry , physics , computer science , statistics , geology , thermodynamics , machine learning , paleontology
SUMMARY 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 P − P 1 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. Copyright © 2011 John Wiley & Sons, Ltd.