Numerical investigation of one-dimensional shallow water flow and sediment transport model using discontinouous Galerkin method

A one-dimensional shallow water flow and sediment transport model is developed using a discontinuous Galerkin finite element scheme. As a first step, four different time marching schemes as well as three different slope limiters have been investigated to find the optimum modeling combination. The efficiency and accuracy of the time marching schemes and slope limiters are quantitatively examined using CPU runtime and comparison between the simulated results and theoretical/experimental data. It is found that using the second order Adam-Bashforth time marching scheme and Monotonized Central method leads to most efficient and accurate results.;As the second part of this research, a novel local time stepping algorithm is introduced. The proposed algorithm allows the maximum possible time advancement based on the CFL criterion within each element. The efficiency of the local time stepping algorithm is examined using CPU runtime and compared with two previously developed local time stepping algorithms. It is found that the proposed algorithm is 30-70% more efficient.;Final part of this dissertation is devoted to sediment transport modeling. A one-dimensional coupled non-equilibrium sediment transport model for unsteady flows in discontinuous Galerkin framework is developed. The model is tested using two experimental tests and shows a good agreement in simulating bed evolution. HLL and HLLC flux functions are modified to include bedload and suspended load sediment fluxes. The performance of the two flux functions is tested. Results show that both functions can predict the flow and morphological changes accurately. The performance of the two empirical formulas, proposed by van Rijn and Zyserman-Fredsoe, for equilibrium near bed concentration of suspended load is investigated. Results indicate that Zyserman-Fredsoe equation can move the hydraulic jump location upstream and improve the water surface simulation.