چكيده به لاتين
In this thesis, a numerical model is developed for solving movable bed shallow water equations. The shallow water equations are obtained from the Navier-Stokes equations by depth integration assuming hydrostatic pressure only and neglecting all dynamic effects in the vertical direction. Such equations can describe the physical behavior of a range of different phenomena in nature. These equations consist of systems of differential equations with partial differential equations of continuity and depth-averaged momentum, and are expressed in terms of the variables of the water level and flow rate from the unit width in one direction or two orthogonal directions in the horizontal plane.
Equations are discretized in the framework of the finite difference method and a two-step predictor-corrector MacCormack Scheme is employed which is a second order accurate scheme both in space and time. In order to prevent unphysical oscillations, the total variation diminishing (TVD) technique is used because it does not require Jacobian matrix and artificial viscosity.The mathematical formulation of this model includes shallow water equations coupled with Exner equation to update the morphodynamic and use of the Grass model for the bed-load discharge.
In order to demonstrate the precision of the MacCormack-TVD method for 1D Dam break, two methods of Lax Wendroff and Lax Friedrich were also used for modeling, which results show a lower oscillation and longer computation time of MacCormack -TVD method than those two methods. Also, for comparing two uncoupled and coupled approaches with moving bed load, have been used three formulas A-CV and A-NC (uncoupled) and C (coupled). In the results of the modeling of this thesis in uncoupled approaches, which was less oscillation than previous studies. To demonstrate the ability of the present model in two-dimensional, modeling the 2D dam break test with fixed bed and conical dune test. In the dam break test, the present model has a better performance than the ADI method used in previous references.
