An adoption of the Spalart–Allmaras turbulence model for two- and three-dimensional free surface environmental flows
Adrien Bourgoin, Kamal El Kadi Abderrezzak, Sofiane Benhamadouche, Riadh Ata
Abstract
In this paper, the Spalart–Allmaras turbulence model, very popular for compressible aerospace applications, is adapted for incompressible free surface environmental flows. The Spalart–Allmaras model is a Reynolds-averaged Navier–Stokes model which solves for one transport equation of a viscosity-like variable. Besides its efficiency and reasonable computational cost, the model can take into account all sources of turbulence production and destruction. The Spalart–Allmaras model was implemented in two- and three-dimensional cases within a massively parallel software. For two-dimensional applications, the Spalart–Allmaras model was used together with the shallow water equations. Although dealing with turbulence with depth-averaged shallow water equations may be perplexing, horizontal turbulent structures could be adequately retrieved. For three-dimensional applications, the Spalart–Allmaras model was introduced with the incompressible Navier–Stokes equations. Numerical resolution is based on a fractional step algorithm that, unlike in a majority of published studies, considers a real free surface, a σ-transform moving mesh and a non-hydrostatic pressure distribution. Numerical resolution uses a mixed finite volume-finite element algorithm. The advection part could be handled, among other options, using a characteristics-based scheme. The Spalart–Allmaras model was validated against experimental laboratory observations and compared to other turbulence models. Results confirmed the potential of the adapted SA turbulence model, as both averaged and fluctuating fields (i.e. kinetic energy and velocity) showed quality comparable to, or even better, than those obtained by the well-known k-ϵ turbulence model.