Date of Award


Document Type


Degree Name

Master of Science (MS)

Legacy Department

Civil Engineering


Khan, Abdul

Committee Member

Khan , Taufiquar

Committee Member

Ravichandran , Nadarajah


A water surface slope limiting scheme is applied to numerically solve the one dimensional shallow water equations with bottom slope source term. The total variation diminishing Runge-Kutta discontinuous Galerkin finite element method with slope limiter schemes based on water surface and water depth are investigated for solving one-dimensional shallow water equations. For each slope limiter, three different Riemann solvers based on HLL, LF, and Roe flux functions are used. The three different solvers with slope limiters based on water surface and water depth are applied to simulate idealized dambreak problem, hydraulic jump, quiescent flow, subcritical flow, supercritical flow, and transcritical flow. The proposed water surface based slope limiter scheme is easy to implement and shows better conservation property compared to the slope limiter based on water depth for the tests. Of the three flux functions, the Roe approximation provides the best results while the LF function proves to be least suitable when used with either slope limiter scheme.