Free surface flow and wave modeling using object oriented C++ finite volume solver on irregular topography with wetting and drying

In this research, both one- and two-dimensional (1D - 2D) free surface flow solvers are developed to simulate the propagation of shock, flood, and solitary waves in domains of flat or variable bottom. A detailed analysis is implemented to solve ID Shallow Water Equations. Two different finite-difference (FD) and finite-volume (FV) schemes used for modeling shock waves are formulated and their performances are evaluated for several dam-break cases. The results obtained from the 1D solver, which is developed using the FORTRAN programming language, show that the solution accuracy and stability from the FV schemes are better than those of FD schemes.;In addition, a 2D cell-centered FV flow solver working on unstructured meshes is developed. Assessment of approximate Riemann solvers is achieved and their performances are compared. First-order, hybrid and second-order accurate schemes in space are utilized and compared for their stability, accuracy and convergence. A mass balance preserving wet/dry boundary solution algorithm is integrated into the numerical scheme to satisfy positive depth and minimize mass errors. Detailed analyses are completed and explained for various schemes that are used to preserve the still water surface level on domains with irregular topography. A class environment created in Object Oriented C++ programming language is presented in detail to show the procedure of building and structuring a flow model. The 2D solver is verified using several test cases over wet and dry lands given in the literature. The solver is then used to model flood event that occurred in 1991 in the Ulus Basin, located in the West Black Sea Region of Turkey. Inundation maps extracted for this event are presented. GIS is used for pre-processing and post-processing purposes.;Moreover, a wave model, which is using FD-FV hybrid scheme for the discretization of the Boussinesq equations, is developed to investigate propagation of solitary waves. This hybrid scheme is applied to simulate head on collisions of two solitary waves and shoaling from deeper to shallower water on regions with a sloping channel bottom. The results are compared with analytical solutions and results from Boussinesq finite element models given in the literature.