Modeling bathymetry changes in the coastal zone - state of knowledge analysis

In this paper we briefly review the mathematical models used to describe the bathymetry changes in time and space. Overview of the models was carried out with particular emphasis on the problems encountered during the nonlinear equation solution, commonly used to describe the morphology of the bottom in the coastal zone of the sea. In contrast to the commonly used approach, it is proposed a linear relationship between volumetric flow of sediments transport rate and thickness of the layer of sediment grains, closely adjacent to each other and staying in motion. This linear relationship allows to precisely define the initial - boundary conditions and to apply the numerical scheme of finite difference method of „upwind” at the accuracy of the first order, not distorted by numerical errors. The author’s method also allows to implement changes to the description of the bathymetry of simultaneous changes in the distributions of the sediment grain size.