МЕТОД ЧИСЕЛЬНОГО МОДЕЛЮВАННЯ ГІДРОДИНАМІЧНИХ ПРОЦЕСІВ

Abstract

This article presents a numerical simulation method that is used in the study of the dynamics of continuous viscous weakly compressed fluids based on the system of equations of continuity and Navier-Stokes. The proposed method uses a complex approach using the numerical solution of the continuity equation by the finite-volume method, and for solving the Navier-Stokes equation the splitting method by physical factors. The article shows that the finite volume method, which was used to describe the flow of both compressed and uncompressed liquids, has such important advantages as the presence of good conservative properties and assumptions of discretization of complex computational domains into simpler ones than isoparametric finite element formulation of the problem or the introduction of generalized coordinates. A component is introduced into the method of splitting according to physical factors, which takes into account the artificial compressibility of the test liquid, which allows you to first calculate the intermediate velocity field, which is then corrected taking into account the pressure gradients. The difference scheme of this method allows one to calculate the flow field without using the values ​​of the vortex and pressure on a solid surface. In the framework of the proposed approach, it is not necessary to calculate the value of the vortex on a solid surface. The latter can be found from the calculated velocity field using any of the difference representations of the expression for the vortex at the boundary points. To confirm the effectiveness of the proposed method, in the FlowVision CFD program, solutions were obtained for a number of problems in external hydrodynamics, using the example of a cylindrical surface optics, which confirmed the stability of the results obtained. This method allows one to compute the flow of flat, axisymmetric, and three-dimensional bodies of a complex configuration with a flow of a viscous weakly compressed fluid, as well as internal flows in a wide range of Reynolds numbers using a single algorithm.