Finite element modelling of free-surface flows with non-hydrostatic pressure andk-ɛ turbulence model

Abstract

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-e 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