Modeling and Visualization of Sedimentation in a Viscous Incompressible Fluid

The article considers the equation of hydrodynamics with a sliding condition at the boundary and the motion of an inertialess non-diffusing impurity in a viscous incompressible liquid in a cylindrical region. Diffusion processes in dispersed systems are investigated – the effect of parachuting a falling large particle in a liquid-filled medium. The result of a numerical and analytical solution of a system of equations consisting of the Navier-Stokes equation for an incompressible fluid and the convection-diffusion equation is presented. It is shown that in order to calculate the trajectory of an impurity particle, it is necessary to solve the Cauchy problem in three-dimensional space with given initial conditions for each impurity particle. A series of computational experiments has been carried out to simulate the dynamics of a heavy impurity in an incompressible liquid. The initial conditions for the Cauchy problem are set based on a black-and-white image, where a black pixel is considered an impurity particle. The developed software has been tested to determine the degree of confidence in the calculations performed by solving the initial problem in reverse order, for which the initial conditions for the Cauchy problem were chosen equal to the value at the last step of the initial problem. A visual and quantitative analysis of the results obtained is presented based on the developed software package using the MathGL library for the C++ programming language.