ABSTRACT
One-dimensional conservation laws In this and the following chapters, the discontinuous Galerkin (DG) method will be applied to numerically solve the shallow water flow problems, which are governed by hyperbolic conservation laws. The scalar and system of conservation laws in one dimension are discussed in this chapter. The method is first applied to the benchmark Burgers’ equation, followed by the application of the DG method to solve the shallow water flow problems in rectangular channels. The total variation diminishing (TVD) slope limiter is presented for the nonlinear conservation laws.
