
49
chapter four
One-dimensional
conservation laws
In this and the following chapters, the discontinuous Galerkin (DG)
method will be applied to numerically solve the shallow water ow prob-
lems, which are governed by hyperbolic conservation laws. The scalar and
system of conservation laws in one dimension are discussed in this chap-
ter. The method is rst applied to the benchmark Burgers’ equation, fol-
lowed by the application of the DG method to solve the shallow water ow
problems in rectangular channels. The total variation diminishing (TVD)
slope limiter is presented for the nonlinear conservation laws.
4.1 Burgers’ equation
Burgers’ equa ...