Abstract
One of the practically important tasks of hydrophysics for sea coastal systems is the problem of modeling and forecasting bottom sediment transportation. A number of problems connected to ship safety traffic, water medium condition near the coastal line etc. depends on forecasting bottom deposit transportation under natural and technogenic influences. Coastal systems are characterized by a complicated form of coastline - the presence of long, narrow and curvilinear peninsulas and bays. Water currents and waves near the beach are strongly depend on complicated coastal line and in turn, exert on the bottom sediment transportation near the shore. The use of rectangular grids in the construction of discrete models leads to significant errors in both the specification of boundary conditions and in the modeling of hydrophysical processes in the coastal zone. In this paper, we consider the construction of a finite-element approximation of the initial-boundary value problem for the spatially two-dimensional linearized equation of sediment transportation using optimal boundary-adaptive grid. First, the linearization of a spatially two-dimensional nonlinear parabolic equation on the time grid is performed-when the coefficients of the equation that are nonlinearly dependent on the bottom relief function are set on the previous time layer, and the corresponding initial conditions are used on the first time layer. The algorithm for constructing the grid is based on the procedure for minimizing the generalized Dirichlet functional. On the constructed grid, finite element approximation using bilinear basis functions is performed, which completes the construction of a discrete model for the given problem. The using of curvilinear boundary adaptive grids leads to decreasing of total grid number in 5-20 times and respectively the total modeling time and/or it allows to improve modeling accuracy.
Highlights
One of the essential features of coastal and marine systems is complicated form of the coastline, which hardly influences on mathematical modelling of these systems
The use of rectangular, does not allow to take into account, with practical value accuracy, the presence narrow sea coastal bodies of complicated shape, such as bays, estuaries, straits, peninsulas etc. The presence of these objects hardly determines the structure of coastal currents, especially for shallow water bodies of the South of Russia, similar to the Azov Sea and Taganrog bay
The linearization of a spatially two-dimensional nonlinear parabolic equation on the time grid is performed, when the coefficients of the equation that depend nonlinearly on the bottom depth function are set on the previous time layer
Summary
One of the essential features of coastal and marine systems is complicated form of the coastline, which hardly influences on mathematical modelling of these systems. The algorithm for constructing the grid is based on the procedure for minimizing the generalized Dirichlet functional This approach has shown its effectiveness in the construction of minimal non degenerate grids for Z-shaped test regions, such as the "Maltese cross", etc., as well as in the numerical solution of problems of hydrodynamics of coastal systems, including in the Azov Sea [9]. In this paper, the finite element method is approximated using the bilinear basis functions of the linearized chain of sediment transport problems applied to the Azov Sea and the Taganrog Bay. Let us consider the equation of sediment transport according to the [10,11,12,13,14,15]:
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
