is playing a peculiar role in such studies , but it is very little in finite volume discretization.

The traditional TVD schemes have different features in the aspects of constructive form and numerical performance. Some are more dissipative and some are more compressive. Through the numerical studies it is shown that good numerical performance and the complicated flow characteristics, such as the reflection and diffraction of dam-break waves can be demonstrated by using a hybrid type of TVD scheme with a proper limiter. In this paper, such type of scheme is extnded to the 2D shallow water equations. A finite volume method on arbitrary quadrilateral elements is presented to solve shallow water flow problems with complex boundaries and having discontinuities.     

2.       GOVERNING EQUATIONS

  The governing equations of shallow water problems can be derived by depth averaging of the Navier-Stokes equations. The conservative form of the shallow water equations is given by

                                               (1a)

where

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