SIMULATION OF FLUID MOTION IN COMPLEX CLOSED SURFACES USING A LATTICE BOLTZMANN MODEL

Abstract

Restorative operations on the human digestive tract can cause negative consequences. These effects were manifested in the appearance of undesirable deformations, so-called "blind bags", which arose as a result of the formation of high pressure zones after the geometry of the digestive tract cavity was changed during reconstructive surgery. For this reason, the development of a mathematical model of the movement of liquids in closed surfaces has become necessary in recent years.

There are many approaches to solving such problems. Most of the traditional approaches require considerable time and computing resources for their implementation. Thus, when using analytical methods, there are possible solutions only under certain conditions. Therefore, there is a need to use effective numerical methods, one of which is the lattice Boltzmann model. The purpose of this work is to study hydrodynamic processes in closed surfaces using the lattice Boltzmann model.

There is a significant number of publications devoted to modeling the movement of liquids in closed surfaces. But the analysis of the publications showed that the use of the Boltzmann lattice model in such problems has not been studied in detail.

Formulated statement of the problem in the form of a numerical solution of the Boltzmann equation. It is proposed to solve such a problem by using the Boltzmann lattice model.

The results of theoretical studies and experiments showed the practical feasibility of using the proposed approach to modeling the movement of liquids in closed surfaces. It is noted that the proposed approach has prospects for further research and development.