equations of this type using the CG finite element method will frequently lead to spurious spatial
oscillations in the solution. To overcome these shortcomings, a number of so-called advection
schemes can be employed (see Iskandarani, et al., 2005 for a review and comparison of some of
the more popular schemes). One such scheme that has received considerable recent attention and
that has been applied successfully to a wide variety of problems is the discontinuous Galerkin
(DG) finite element method.
Originally developed by Reed and Hill (1973), but more recently expounded on in a
series of papers by Cockburn, et al. (see the review article by Cockburn and Shu, 2001 and the
references therein), the DG method uses trial and test function spaces that are continuous over a
given element but which allow discontinuities between elements. This results in a block diagonal
or, with an appropriate choice of basis, diagonal mass matrix that can be trivially inverted.
Communication between elements is accomplished via a so-called numerical flux, which for the
case of a scalar equation can be defined using upwinding techniques. The method is also "locally
conservative", meaning that the conservation of the transported quantity is satisfied on a local or
elemental level. This has been shown to be a desirable property when coupling flow and
transport algorithms (see for example Dawson, et al., 2004)
In this paper, we present the implementation and verification of a DG sediment
transport/morphological model that is coupled to the ADCIRC hydrodynamic model. We note
that this sediment transport model is just one component of a suite of DG model components that
are currently being developed for flow and transport, which will form a completely DG based
morphodynamic modeling system with both h (grid size) and p (polynomial order) refinement
options. In this paper, we restrict our attention to the second-order (p = 1) case for the sediment
transport model, but we note that p-refinement is easily implemented within the framework of the
DG method (see Kubatko, et al., 2005 for an example of this for the shallow water equations).
This paper is organized as follows. In Section 2, we describe the mathematical model
defining the sediment transport and morphological evolution of the bed which consists of the
3
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