Development of a coupled depth averaged-rans 3D model for open channel flow using higher-order upwinding schemes

Abstract

The analysis of flow in open channels is of fundamental importance in river engineering and related areas. In numerical simulations of open channels, predictions of flow conditions are generally conducted through one and two-dimensional depth-averaged (DA) models. While the 2D models are relatively simpler and require less computational effort, they fall short in representing complex flow phenomena, where the flow field has highly non-uniform velocity and non-hydrostatic pressure, which requires the use of complete three-dimensional models. However, 3D modeling can be more computationally intensive and require sophisticated techniques. In an effort todevelop a 3D river model requiring computational time comparable to that of 2D models, a novel approach was formulated by coupling both DA and 3D Reynolds-Averaged Navier-Stokes (RANS) model, that enabled faster convergencebut at the same time provided high accuracy of 3D models. However, the RANS 3D model used only the first-order upwind method to resolve theadvective terms, which, although stable in simulating advection, are also known to suffer from excessive numerical diffusion. In the present study,a RANS 3D model is developed by implementing higher-order discretization of the convective terms. To select suitable higher-order schemes for the RANS model, at first, thirty higher-order schemes were tested for pure advection as a preliminary assessment of the methods against the analytical solution in a simpler context. Thebest performing five methods were identified asthe Adaptive stencil, Superbee, fifth-order upwinding with limiter, QUICKEST, and MUSCL schemes. For one of the test cases with triangular distribution, the normalized root mean square error(NRMSE) and the normalized variance(NV) index for the first-order upwinding method were calculated to be 10.09 and -10.37, respectively. Whereas for the same test case, NRMSE valueswere in the range of 1.93 to 3.45 for the top five schemes, suggesting reasonably good accuracy, and NV indices were within ±0.5, indicating that they were neither too diffusive nor compressive. The best-performing methods were then selected and used in the RANSmodel. Initially, performance of the higher-order schemes were investigated for various 2D plane flow scenarios, where the flow varied only in the longitudinal and vertical directions. The model was verified with experimental results of flow development, flow over a symmetric hump and series of dunes. The validated model was then used to simulate synthetic scenarios of flow over dunes in long reaches with different numerical grid coarseness in the longitudinal flow direction. The higher-order schemes resulted in 20-30% better results for coarser grid resolution, especially the second-order upwind, Adaptive and QUICKEST schemes. Finally, the 3D model was developed with these selected higher-order schemes and different flow scenarios were simulated. The higher-order methods provided more accurate solutions against the mesh-independent solution than the first-order differencing methods.A comparative analysis was also done, withgradual coarsening of the numerical grid, between the increased savings in computational time and the associated accuracy of flow variables, and the QUICKEST scheme was found to perform better than the other methods.The upgraded 3D model with selected higher-order schemes was also used to simulate a real case open channel flow scenario of Padma River near NariaUpazila. The 3D model provided almost a 10-15% increase in the overall surface velocity of the channel from the 2D depth-averaged model and at the same time, significantly higher bed shear stress was observed in some locations. Near-bed vortex was also simulated in the 3D model which may cause undercut of bank and increases the potential for bank erosion. The 3D model was able to provide a greater level of information regarding the flow variables while at the same time having a computational time comparable to that of a 2D model.