1st Edition
Modeling Shallow Water Flows Using the Discontinuous Galerkin Method
Introduction
A historical overview
Organization of the book
References
General formulation of the discontinuous Galerkin method
Conservation form of equations
Shape functions
Isoparametric mapping
Numerical integration
Approximate Riemann solvers
Time integration
References
Discontinuous Galerkin method for one-dimensional nonconservative equations
Discontinuous Galerkin method for ordinary differential equations
1D Linear convection
1D Transient diffusion
1D Steady diffusion
References
One-dimensional conservation laws
Burgers’ equation
Total variation diminishing slope limiter
Shallow water flow equations in rectangular channels
DG method for shallow water flow equations
Numerical tests
References
One-dimensional shallow water flow in nonrectangular channels
General form of the Saint Venant equations
Discontinuous Galerkin method for general Saint Venant equations
Numerical tests
References
Two-dimensional conservation laws
Pure convection in 2D
Governing equation of convection in 2D
Discontinuous Galerkin formulation for 2D convection
Slope limiters
Numerical tests
References
Two-dimensional shallow water flow in channels with horizontal beds
Two-dimensional shallow water flow equations for a horizontal bed channel
Numerical flux
Dry bed treatment
Numerical tests
References
Two-dimensional shallow water flow in channels with bed variations
Two-dimensional shallow water flow equations for natural channels
Numerical flux and source term treatment
Numerical tests in channels with irregular beds
References
Pollutant transport
Pollutant transport in 1D
Pollutant transport in 2D
References
Concluding remarks
Summary
Current research topics
References
Index
Biography
Abdul A. Khan, Ph.D., is an associate professor in the Glenn Department of Civil Engineering at Clemson University (South Carolina). He received a Ph.D. from the University of Alberta, Edmonton, Canada. After his Ph.D., Dr. Khan worked at the National Center for Computational Hydroscience and Engineering, University of Mississippi, before moving to Clemson University. He has been working in the area of computational modeling of river hydraulics, dam-break flows, and sediment transport for the past 20 years. He has published close to 50 journal articles related to his research work and several papers on river flood and dam-break flow modeling.
Wencong Lai, Ph.D., earned a Ph.D. (2012) and an M.S. (2010) in civil engineering from Clemson University, in the area of applied fluid mechanics, and a B.E. (2008) in water conservancy and hydropower engineering from Huazhong University of Science and Technology, China. He is currently a postdoctorate research associate at the University of Wyoming and a member of the CI-WATER’s High-Resolution Multi-Physics Watershed Modeling team. Dr. Lai’s research focuses on computational hydraulics and hydrology. He has developed numerical models for shallow water flows in natural rivers and watersheds using the discontinuous Galerkin finite element method.
