Modeling Shallow Water Flows Using the Discontinuous Galerkin Method

ISBN: 9781138076464 出版年：2014 页码：208 Khan, Abdul A Lai, Wencong CRC Press

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