Geodesic
Regularized difference scheme for solving hydrodynamic problems
Matematičeskoe modelirovanie, Tome 34 (2022) no. 2, pp. 85-100.

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The paper considers a three-dimensional hydrodynamic model of the movement of an aqueous medium, which includes the Navier – Stokes equations of motion, including the regularized continuity equation, taking into account the effect of the impurity on the density of the aquatic environment. The approximation of the equations for calculating the velocity field of the aquatic environment with respect to spatial variables was carried out on the basis of splitting schemes for physical processes taking into account the filling factors of control plots, which made it possible to take into account the complex geometry of the coastline and the bottom of the reservoir, as well as to improve the accuracy of modeling. Calculation of the pressure field using a regularizer in the continuity equation made it possible to increase the accuracy of modeling: in the developed model, pressure cannot propagate faster than the velocity of the shock front (in the linear approximation of the speed of sound). The application of this approach also makes it possible to reduce the computational complexity of solving grid equations for the problem of calculating pressure due to the presence of a diagonal dominance in the matrix of coefficients. Numerical experiments were carried out to simulate the movement of the aquatic environment in the estuary area and the process of mixing waters in the presence of a significant density gradient in the aquatic environment.
Keywords: model of hydrodynamics, continuity equation, regularization, Upwind Leapfrog difference scheme, Standard Leapfrog difference scheme. 
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     title = {Regularized difference scheme for solving hydrodynamic problems},
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A. I. Sukhinov; A. E. Chistyakov; I. Y. Kuznetsova; A. M. Atayan; A. V. Nikitina. Regularized difference scheme for solving hydrodynamic problems. Matematičeskoe modelirovanie, Tome 34 (2022) no. 2, pp. 85-100. http://geodesic.mathdoc.fr/item/MM_2022_34_2_a6/

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