Numerical model simulations of channel flow for the South Saskatchewan River, Canada

The aim of these CFD simulations was to investigate the effect of dunes on the depth-averaged and near-bed flow fields. To accomplish this, simulations were conducted using two meshes: one using high resolution measured channel morphology that included dunes, and one with the dune-scale morphology removed from the model domain. A digital elevation model (DEM) for the model domain was constructed from specially commissioned aerial imagery (pixel resolution 0.06 m) captured at a height of ~1500 m from a fixed-wing airplane with an UltraCamXp sensor. A 0.06 m resolution DEM was constructed using a combination of large format Structure-from-Motion (SfM) photogrammetry (using the commercial software Pix4D) and a regression model between water-depth and image brightness (see Strick et al., 2019). SfM techniques were applied to generate a DEM in emergent areas and in a narrow section along one channel bank where the river bed is composed predominantly of gravel. A depth-brightness model was applied in all other areas to calculate water depth from pixel brightness in the aerial imagery. The DEMs generated using SfM and the depth-brightness model were merged to produce a single DEM for use in CFD mesh generation. To remove dunes from the original 0.06 m resolution DEM constructed from aerial photography without affecting the representation of bank or bar topography, the outlines of the banks and bar fronts were identified visually in ARCMAP, and raster masks produced to separate each bar surface for individual filtering. River banks and the bar lee slopes of the unit bars were therefore not modified. To remove the dunes from the individual bar tops a moving-average, weighted-mean filter was used, with a window size of 6 m x 1 m, with the longest axis in the downstream direction, parallel to dune length. Two structured, finite volume CFD meshes were then constructed (one including dune morphology and one with dunes removed) for CFD modelling, both comprised of 4948 x 1172 x 20 cells in the downstream, cross-stream and vertical directions respectively. Horizontal mesh resolution was an average of 8 cm with 20 cells in the vertical and a planar water surface (at 0 m depth).

Modelling was carried out using the open source CFD package OpenFOAM to solve the three-dimensional Navier-Stokes equations with a Re-Normalization Group (RNG) k-epsilon turbulence closure. The free surface was represented in the model with a rigid-lid approximation. Inlet conditions were defined using measured flow velocities. A Neumann pressure condition was set at the outlet. Second order central differencing numerical schemes were used for gradients, second order bounded central differencing for divergence; and an unbounded second order deferred corrected scheme for the Laplacian surface normal gradients were employed. Convergence criteria were iteratively tested and set to a tolerance of 1x10-8 for pressure and 1x10-10 for velocity, k and epsilon. Solver tolerances were set to 1x10-10 for pressure and 1x10-12 for velocity. The results of two simulations are included here.

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