Regularized Difference Scheme for Solving Hydrodynamic Problems

摘要

Abstract A description is given of a three-dimensional model of hydrodynamics of the motion of an aquatic medium, which includes the Navier–Stokes equations of motion, including a regularized continuity equation that takes into account the effect of impurities on the density of the aquatic medium. The equations for calculating the velocity field of the aquatic environment in terms of spatial variables are approximated based on the splitting schemes for physical processes, taking into account the filling factors of the control areas, which makes it possible to take into account the complex geometry of the coastline and the bottom of the reservoir, as well as improve the accuracy of the modeling. Calculation of the pressure field using a regularizer in the continuity equation makes it possible to improve the accuracy of the modeling: in the developed model, pressure cannot propagate faster than the shock front velocity (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 pressure calculation problem due to the presence of diagonal dominance in the matrix of coefficients. Numerical experiments are 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 of the aquatic environment.