Aspects of numerical solution of the unsteady problem of fluid wind motion
UDC
51.7DOI:
https://doi.org/10.31429/vestnik-20-1-12-18Abstract
The paper presents computational approaches for solving the unsteady test problem of wind motion of a fluid. When integrating a non-stationary inhomogeneous model, its solution is considered as the sum of solutions of a stationary inhomogeneous equation and a solution of a homogeneous non-stationary analog. The stationary inhomogeneous equation for the current function is approximated based on the Ilyin scheme and solved iteratively. To determine the variable component of the solution, a Sobolev type equation is obtained that is not resolved with respect to the time derivative. When implementing discrete models of ocean dynamics to solve specific problems, various model calculations are most often compared with each other, based on available data on the dynamics of waters in a given area and based on the experience and preferences of researchers. The presence of an exact solution to a particular problem allows you to objectively make such a choice. In this paper, some computational approaches are proposed for solving a non-stationary problem for further comparison with the obtained analytical "exact" solution. For the unsteady problem of the Ekman type wind circulation, analytical solutions are obtained for a space-variable wind effect. A numerical implementation algorithm is constructed to find an approximate solution. The results can be used in the construction of numerical models of the dynamics of the ocean and various reservoirs.
Keywords:
dimensionless problem, wind currents, test problem, analytical solution, current function, integral velocityAcknowledgement
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