The overtopping or partial breaching flow of a dike is distinguished by an unsteady flow with discontinuity. In this paper, 1-D and 2-D flow mathematical models are established, and the governing equations of these models take the effect of a steep bottom slope on the flow movement into consideration. Then a MacCormack-TVD scheme for 1-D dam-break flow is extended and applied to solve the governing equations for 2-D dike overtopping and partial breaching flows. To verify its validity, the numerical results are compared with the analytical solution, and good agreements are obtained. It shows that the calculated results are obliviously larger without accounting for the effect of the steep bottom slope.
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