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Finite element modelling of free‐surface flows with non‐hydrostatic pressure and k – ε turbulence model
Author(s) -
Leupi C.,
Altinakar M. S.
Publication year - 2005
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.986
Subject(s) - free surface , turbulence , mechanics , turbulence modeling , geology , open channel flow , reynolds stress , computational fluid dynamics , geometry , mathematics , physics
Validation of 3D finite element model for free‐surface flow is conducted using a high quality and high spatial resolution data set. The commonly numerical models with the conventional hydrostatic pressure still remain the most widely used approach for the solution of practical engineering problems. However, when a 3D description of the velocity field is required, it is useful to resort to a more accurate model in which the hydrostatic assumption is removed. The present research finds its motivation in the increasing need for efficient management of geophysical flows such as estuaries (multiphase fluid flow) or natural rivers with the presence of short waves and/or strong bathymetry gradient, and/or strong channel curvature. A numerical solution is based on the unsteady Reynolds‐averaged Navier–Stokes equations on the unstructured grid. The eddy viscosity is calculated from the efficient k – ε turbulence model. The model uses implicit fractional step time stepping, and the characteristics method is used to compute the convection terms in the multi‐layers system (suitable for the vertical stratified fluid flow), in which the vertical grid is located at predefined heights and the number of elements in the water column depends on water depth. The bottommost and topmost elements of variable height allow a faithful representation of the bed and the time‐varying free‐surface, respectively. The model is applied to the 3D open channel flows of various complexity, for which experimental data are available for comparison. Computations with and without non‐hydrostatic are compared for the same trench to test the validity of the conventional hydrostatic pressure assumption. Good agreement is found between numerical computations and experiments. Copyright © 2005 John Wiley & Sons, Ltd.