Software for solving the Cauchy problem and visualizing heavy impurity flow simulation results

This paper presents a method for data preparation and visualization of the solution to the Cauchy problem, which arises in simulating the dynamics of impurities in potential flows and in a viscous incompressible liquid within a cylindrical flow region. The Cauchy problem was solved using the 4th-order Runge-Kutta method. We developed software that solves the Cauchy problem in 3D space and automatically visualizes the results. This method can simulate the dynamics of an inertialess, non-diffusing impurity in a liquid, provided that the vector field $\vec{V}$, which solves the Cauchy problem, satisfies the hydrodynamics equations. The problem is considered for the entire set of initial data defining the impurity distribution at the initial time. The software performs calculations distributed over available computer cores using OpenMP. The MathGL library was employed for visualization. The paper also presents the results of software testing.