Study of 3D discrete hydrodynamics models using cell filling

¹ Don State Technical University, 1 Gagarina sq., Rostov-on-Don, 344003, Russia
² Taganrog Institute, named after A.P. Chekhov – branch of Rostov State University of Economics, Taganrog, Russia

^* Corresponding author: sukhinov@gmail.com

Abstract

Modern methods and tools for coastal hydrodynamics modeling indicate the necessity of constructing discrete analogs of models for ones the properties: balance and conservation laws (for mass, flows, impulse), stability, convergence and etc. have been fulfilled. The paper considers a continuous three-dimensional mathematical model of the hydrodynamics of water basins and its discretization. The pressure correction method at variable water medium density was used to solve the problem of hydrodynamics. The considered discrete mathematical models of hydrodynamics take into account the filling of control cells on rectangular grids. This increased the accuracy of the solution in the case of complex geometry by improving the boundary approximation. From the obtained estimates of the components of the velocity vector, it follows that there are no two or more stationary regimes in which all forces are balanced, and the solution to the discrete problem exists and is unique and tends to the solution of the continuous problem upon reaching the stationary regime. Also the balance of the flows for the discrete model has been proved as well as absence of non-conservative dissipative terms.