Wave propagation on coral reef topography with abrupt change of water depth is quite different from that on slow change of water depth. In this paper, the research progress of wave propagation on coral reef topography with abrupt change of water depth is reviewed, and the process of transforming general Boussinesq equation into conservation type governing equation is described in detail. The governing equation format is introduced: the mixed solution of finite difference method and finite volume method is adopted, the convection term in the equation is discretized by finite volume method, the interface flux is solved by HLL Riemannian solution, and the left and right variables of the control unit boundary are constructed by the fourth-order state interpolation method (muscl). Some existing problems and further research directions are pointed out.