Depth Averaged and RANS Modeling of Open Channel Flow.

摘要

This study focuses on two issues of open channel flow modeling. First the convergence behavior of preconditioned Krylov subspace methods: Generalized Minimal Residual (GMRES) and Bi-Conjugate Gradient Stabilized (BiCGSTAB) is investigated for the open channel flow model River2D with Jacobi, Symmetric Gauss-Seidel (SGS) and Incomplete Lower Upper (ILU) factorizations with different levels of fill as preconditioners. A novel technique is developed where a matrix obtained from a lower time step than the simulation time step is used to compute the ILU factors. This technique increases the robustness and efficiency of the ILU preconditioners significantly. Applying this technique to ILU, the performance of preconditioned GMRES and BiCGSTAB are compared. In most cases ILU with no fill is found to be the most efficient preconditioner. A test to investigate the effect of mesh refinement on the convergence of the new ILU preconditioned solvers also shows promising results.;The second issue concerns with a coupled depth averaged (DA) and Reynolds averaged Navier-Stokes (RANS) model developed for open channel flow with or without the assumption of hydrostatic pressure. Initially the water surface and DA velocity are estimated by a DA model neglecting non-uniform velocity and non-hydrostatic pressure. Then in the RANS model, the horizontal momentum and the continuity equations are solved for the horizontal and vertical velocity respectively with the water surface as a fixed zero pressure boundary. For the non-hydrostatic RANS model the pressure Poisson equation is solved for the non-hydrostatic pressure. A correction term is introduced in the RANS horizontal momentum equations for mass balance. Once the RANS model results are available, DA model results can be updated iteratively by incorporating the effects of non-uniform velocity and non-hydrostatic pressure. First the model is developed for two dimensional plane flow and verified against the experimental results of flow development, flow over a symmetric hump and a dune with good results and excellent computational efficiency. Then the model is extended and tested for three dimensional flow with promising results.