Mathematical modeling of hydrodynamic processes in the coastal waters of the Sea of Japan

A three-dimensional mathematical model of coastal water dynamics in the Peter the Great Bay of the Sea of Japan is presented. The system of Navier-Stokes equations is written under the assumption of a hydrodynamic approximation of an inhomogeneous fluid and takes into account turbulent exchange, wind stresses, friction forces, complex topography of the bottom and coastline. On the basis of hydrographic information, a numerical method is used to reconstruct the bottom topography and coastline. The free water surface equation is replaced by a singularly perturbed problem. In the FreeFem++ application software package, a code was written for calculating the hydrodynamic characteristics of coastal waters. During the solution, the finite element mesh is built automatically, the mesh parameters are set by the user. To solve the singular problem, at each time layer, the grid is adapted around the numerical solution with the grid adaptation parameters.