To simulate the dynamical structures of stratified shear flows, the high-resolution Total Variation Diminishing (TVD) method is necessary and widely-used due to its high-order spatial accuracy, oscillation control, and ability to capture the well-defined structures of vortices. Lack of understanding the TVD slope limiters usually results in inaccurate numerical simulation on stratified shear flows in terms of shear instability and spatiotemporal variations of mixing. In this study, the performances of four typical TVD slope limiters, namely the minmod, van Leer, Monotonized Central (MC), and superbee limiters, were investigated on modelling stratified shear flows based on the open-source non-hydrostatic model, NHWAVE. The four slope limiters are all commonly-used and have the typical numerical characteristics. All the limiters were respectively applied in two classical test cases, namely, shear instability and lock-exchange problem. The simulation results showed that the effects of slope limiters were correlated with their characteristics of numerical dissipation (or anti-dissipation), which can influence notably the model predictions of the generation of shear instability, the development of interfacial structures, and the mixing process. In the test cases, MC limiter’s performance was the best, because it could simulate the well-defined structures of instability while not introducing noticeable error. Minmod has an excessively large dissipation, which introduced noticeable numerical errors that can influence the model accuracy and can even suppress or omit the generation of interfacial vortices. Superbee limiter, the most anti-dissipative one, usually over-predicted the instability and mixing effects in time and space domain, and was likely to cause computational instability in some cases. The performances of van Leer and MC were similar, but their predictions of the evolutions of interfacial structures and mixing could be significantly different. Besides, the co-effects of grid resolution and slope limiters were also investigated; it was found that the refinement of grids may not help to reproduce a higher-quality result with a specific slope limiter.

The process of pollutant mixing is significantly influenced by secondary flow and turbulence in meandering rivers. To investigate the influence of different point source release positions on the pollutant mixing process in sinuous open channel flows, a 3D large-eddy simulation (LES) model based on OpenFOAM was established to simulate the process of passive scalar transport in a sinuous channel with a rectangular cross-section. After verification by a flume experiment, two sets of cases in which the point sources were arranged at identical intervals in spanwise and streamwise directions were configured to evaluate the mixing efficiency. The effect of flow structure, secondary motion, and the turbulent viscosity on the scalar transport and mixing was discussed. The distribution of scalar as well as the scalar flux was analyzed in detail, and the fluctuation characteristics were also described. The results demonstrate that due to the existence of secondary flow in the sinuous channel, different transverse and streamwise release positions of the point source have significant influence on mixing efficiency and spatial distribution of the pollutant. The point source placed near the center of the cross-section in transverse or near the apex of the bend in streamwise result in higher mixing efficiency. Mixing efficiency calculated by different indices can be different, which requires comprehensive assessment.

Understanding the transport of point source solutes across the sediment–water interface (SWI) is important for the protection of river environments. Conventional coupled models assume the porous media layer as Darcy's laminar flow and therefore cannot accurately capture the transport processes within the porous media. Furthermore, the effect of the porous structure of the riverbed on the transport process is largely unknown. In this study, we performed pore-scale numerical simulations of point source solutes transport across the SWI to investigate the effects of different porous structures in the riverbed on flow and point source dispersion. By solving the Reynolds-averaged Navier–Stokes equations with the k–ω shear stress transport turbulence closure model, we determine the complex flow field information and the spatial distribution of point source solutes for the coupled model. The results indicate that the presence of porous structures creates recirculation zones in the coupled model, which prevents turbulent structures reaching deeper layers. Random porous structures induce more preferential flow, inhibit the formation of recirculation zones, and exhibit higher solute dispersion, which is directly related to turbulent solute fluxes. Furthermore, our study reveals that the release position of point sources significantly influences the distribution of solute concentrations within the porous bed.