Evaluation of turbulence models in the simulation of oblique standing shock waves in supercritical channel flows

In this article, the two-dimensional depth-averaged Saint Venant equations, including the turbulence terms, are solved in a supercritical flow with oblique standing waves. The algorithm applies the finite volume Roe-TVD method with unstructured triangular cells. Three depth-averaged turbulence models, including the mixing length, and algebraic stress model (ASM), are used to close the hydrodynamic equations. The supercritical flow in a channel downstream from a side-baffle in plan is then simulated, and the numerical results are compared with the data obtained from a laboratory model. The application of different models demonstrates that the consideration of turbulence models improves the results at the shock wave positions. The qualitative study of the results and error analysis indicates that the ASM offers the most desirable solutions in comparison with the other models. However, our numerical experiments show that, amongst the source term components, the negligence of turbulence terms produces the least error in the depth estimation in comparison with the removal of the bed slope or bed friction terms.