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chapter six
Two-dimensional
conservation laws
Formulations of the discontinuous Galerkin (DG) method for a two-
dimensional (2D) scalar equation and equations representing a system of
conservation laws in two dimensions are presented in this chapter. The
treatment of ux terms is discussed. The implementation of different
slope limiters is shown. Details of the numerical solution with the dis-
continuous Galerkin method for pure convection problems and shallow
water ow equations in 2D are discussed.
6.1 Pure convection in 2D
In this section, the governing equation and properties of pure convection
in 2D are discussed. The details of the nu