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We present a fully coupled level set and volume of fluid method for free surface flow simulations on unstructured grids in two- and three-dimensions. The evolution of the level set function and the volume fraction are updated at each time step. The level set advection equation is solved by a least squares weighted residual method while the volume fraction advection is solved using an unsplit Eulerian-Lagrangian scheme. The reconstruction of the interface in the volume of fluid method is performed using the volume fraction information together with the normal vector obtained from the level set function. The reconstructed interface is then used to reinitialize the level set function. Thanks to the fully coupling of the two methods, the interface reconstruction is carried out efficiently and the mass conservation is preserved exactly. The proposed method is validated against several benchmarks and is coupled with the incompressible Navier-Stokes solver to solve two-phase flow problems. Numerical results show that the method is capable of resolving complex interface changes efficiently and accurately.

We report novel results of a numerical experiment designed for examining the basin-scale hydrodynamics that control the mass, momentum, and energy distribution in a daily wind-forced, small thermally-stratified basin. For this purpose, the 3-D Boussinesq equations of motion were numerically solved using large-eddy simulation (LES) in a simplified (trapezoidal) stratified basin to compute the flow driven by a periodic wind shear stress working at the free surface along the principal axis. The domain and flow parameters of the LES experiment were chosen based on the conditions observed during summer in Lake Alpnach, Switzerland. We examine the diurnal circulation once the flow becomes quasi-periodic. First, the LES results show good agreement with available observations of internal seiching, boundary layer currents, vertical distribution of kinetic energy dissipation and effective diffusivity. Second, we investigated the wind-driven baroclinic cross-shore exchange. Results reveal that a near-resonant regime, arising from the coupling of the periodic wind-forcing ( $$T=24$$ h) and the V2H1 basin-scale internal seiche ( $$T_{{\mathrm{V2H1}}}\approx 24$$ h), leads to an active cross-shore circulation that can fully renew near-bottom waters at diurnal scale. Finally, we estimated the bulk mixing efficiency, $$\varGamma$$ , of relevant zones, finding high spatial variability both for the turbulence intensity and the rate of mixing ( $$10^{-3}\le \varGamma \le 10^{-1}$$ ). In particular, significant temporal variability along the slopes of the basin was controlled by the periodic along-slope currents resulting from the V2H1 internal seiche.

In the present study, 2-D large eddy simulations (LES) are conducted for flow past a porous circular array with a solid volume fraction (SVF) of 8.8%, 15.4% and 21.5%. Such simulations are relevant to understanding flow in natural streams and channels containing patches of emerged vegetation. In the simulations discussed in the paper, the porous cylinder of diameter D contains a variable number of identical solid circular cylinders (rigid plant stems) of diameter d = 0.048D. Most of the simulations are conducted at a Reynolds number of 2 100 based on the diameter D and the velocity of the steady uniform incoming flow. Though in all cases wake billows are shed in the regions where the separated shear layers (SSLs) forming on the sides of the porous cylinder interact, the effect of these wake billows on the mean drag is different. While in the high SVF case (21.5%), the total drag force oscillates quasi-regularly in time, similar to the canonical case of a large solid cylinder, in the cases with a lower SVF the shedding of the wake billows takes place sufficiently far from the cylinder such that the unsteady component of the total drag force is negligible. The mean amplitude of the oscillations of the drag force on the individual cylinders is the largest in a streamwise band centered around the center of the porous cylinder, where the wake to wake interactions are the strongest. In all cases the maximum drag force on the individual cylinders is the largest for the cylinders directly exposed to the flow, but this force is always smaller than the one induced on a small isolated cylinder and the average magnitude of the force on the cylinders directly exposed to the flow decreases monotonically with the increase in the SVF. Predictions of the global drag coefficients, Strouhal numbers associated with the wake vortex shedding and individual forces on the cylinders in the array from the present LES are in very good agreement with those of 2-D direct numerical simulations conducted on finer meshes, which suggests LES is a better option to numerically investigate flow in channels containing canopy patches, given that LES is computationally much less expensive than DNS at high Reynolds number. To prove this point, the paper also discusses results of 2-D LES conducted at a much higher Reynolds number, where the near-wake flow is strongly turbulent. For the higher Reynolds number cases, where the influence of the turbulence model is important, the effect of the sub-grid scale model and the predictive capabilities of the unsteady Reynolds averaged Navier-Stokes (RANS) approach to predict flow past porous cylinders are discussed.