INTRODUCTION cont'd - Kubatko_Ocean_Modelling0004

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INTRODUCTION - Kubatko_Ocean_Modelling0003

INTRODUCTION cont'd - Kubatko_Ocean_Modelling0005

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needed leads to improved accuracy for a given computational cost as compared to models that use

structured grid methods. However, both structured and unstructured grid method solutions to the

governing morphological equation can experience numerical robustness and accuracy problems

manifested in the form of spurious spatial oscillations, especially in the presence of steep

bathymetric gradients (see for example Johnson and Zyserman, 2002).

In this paper, we describe the development of a new unstructured grid morphodynamic

model system that uses a new class of highly accurate finite element methods for the solution of

the governing morphological equation. The hydrodynamic model component of our system is

provided by the well verified and validated unstructured grid model ADCIRC, developed by the

second author and a number of collaborators (Luettich and Westerink, 2004). ADCIRC is both a

two-dimensional, depth-integrated (2DDI) and three-dimensional (3D) free surface flow model.

In this paper, we focus specifically on the 2DDI ADCIRC model, which solves the shallow water

equations using the standard or continuous Galerkin (CG) finite element method in space. To

overcome well known problems in solving the shallow water equations using equal-order

interpolating spaces with the CG finite element method, the continuity equation is replaced by the

so-called generalized wave continuity equation (GWCE) (Lynch and Gray, 1979 and Kinnmark,

1986). The solution strategy used in ADCIRC has proven to be robust and computationally

efficient, and it has been validated in a large number of cases (see for example Blain, et al., 1994;

Westerink et al., 1994; Mukai, et al., 2002; Westerink et al., 2004).

Working with a well established hydrodynamic model then, the main focus of this paper

is the development and verification of a bed load sediment transport/morphological model

component to work in conjunction with ADCIRC. Mathematically, the morphological evolution

of the bed is defined by the so-called sediment continuity or Exner equation. This equation

simply states that the time rate of change of the bed elevation is equal to the divergence of the

sediment flux, which can be expressed in terms of the local flow properties through the use of an

empirical sediment transport formula. As is well known, solving advection dominated transport

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