Premium
A comparison of primitive variables and streamfunction–vorticity for fem depth‐averaged modelling of steady flow
Author(s) -
DeVantier Bruce A.
Publication year - 1989
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.1650091106
Subject(s) - vorticity , inflow , stream function , turbulence modeling , mathematics , turbulence , flow (mathematics) , viscosity , variable (mathematics) , vorticity equation , finite element method , mechanics , mathematical analysis , geometry , vortex , physics , thermodynamics
The governing equations for depth‐averaged turbulent flow are presented in both the primitive variable and streamfunction–vorticity forms. Finite element formulations are presented, with special emphasis on the handling of bottom stress terms and spatially varying eddy viscosity. The primitive variable formulation is found to be preferable because of its flexibility in handling spatial variation in viscosity, variability in water surface elevations, and inflow and outflow boundaries. The substantial reduction in computational effort afforded by the streamfunction–vorticity formulation is found not to be sufficient to recommend its use for general depth‐averaged flows. For those flows in which the surface can be approximated as a fixed level surface, the streamfunction–vorticity form can produce results equivalent to the primitive variable form as long as turbulent viscosity can be estimated as a constant.