Context. Recently, the number of reconstructive operations on the digestive tract has significantly increased. Such operations have<br />predictable negative consequences associated with disruptions of hydrodynamic processes in the anastomosis area. These negative consequences can be partially avoided by choosing anastomosis anatomical form based on mathematical modeling. Known mathematical models are cumbersome and do not allow to obtain results in real time. The proposed approach using lattice Boltzmann method allows solving this problem.<br />Objective. The purpose of the work is to develop a three-dimensional mathematical model of anastomosis for research of hydrodynamic<br />parameters of fluids with complex structure in real time.<br />Method. The method of constructing and analyzing the mathematical model of anastomosis of the digestive tract based on lattice<br />Boltzmann method is proposed. The method differs in that it provides simultaneous analysis of hydrodynamic parameters of the liquid and<br />determines the nature of movement of fine-grained inclusions in the anastomosis area. The main stages of the method are the development of technology for determining the modeling area, discretization of the three-dimensional Boltzmann equation with the choice of lattice and the nature of the collision operator, taking into account the complex structure of the liquid; development of the technology of transition from the density distribution function to the distribution of pressure at the mesoscopic level, taking into account the properties of the liquid, the creation of the process of transforming the set of mesoscopic parameters into the macroscopic parameters of the liquid. Results include determining the distribution of the velocity field in the anastomosis area to modify its geometry. The study of the<br />influence of gravity on the nature of motion of fine-grained inclusions has been carried out. The quantitative characteristics of the delay<br />of particles in the area of anastomosis, depending on the dynamic viscosity of the liquid, are determined.<br />Conclusions. The three-dimensional mathematical model discussed in this paper is based on the application of the lattice Boltzmann<br />method for calculating the hydrodynamic parameters of the motion of fluid in the study area. The distinctive feature of the model is that<br />it accounts for the complex nature of the liquid having fine-grained inclusions. The model allows determining the behavior of these<br />inclusions and the field of speed with sufficient accuracy in real time.
Науковий журнал «Радіоелектроніка, інформатика, управління»
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Novotarskyi, M. A.; National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine Stirenko, S. G.; National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine Gordienko, Y. G.; National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine |
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Context. Recently, the number of reconstructive operations on the digestive tract has significantly increased. Such operations have<br />predictable negative consequences associated with disruptions of hydrodynamic processes in the anastomosis area. These negative consequences can be partially avoided by choosing anastomosis anatomical form based on mathematical modeling. Known mathematical models are cumbersome and do not allow to obtain results in real time. The proposed approach using lattice Boltzmann method allows solving this problem.<br />Objective. The purpose of the work is to develop a three-dimensional mathematical model of anastomosis for research of hydrodynamic<br />parameters of fluids with complex structure in real time.<br />Method. The method of constructing and analyzing the mathematical model of anastomosis of the digestive tract based on lattice<br />Boltzmann method is proposed. The method differs in that it provides simultaneous analysis of hydrodynamic parameters of the liquid and<br />determines the nature of movement of fine-grained inclusions in the anastomosis area. The main stages of the method are the development of technology for determining the modeling area, discretization of the three-dimensional Boltzmann equation with the choice of lattice and the nature of the collision operator, taking into account the complex structure of the liquid; development of the technology of transition from the density distribution function to the distribution of pressure at the mesoscopic level, taking into account the properties of the liquid, the creation of the process of transforming the set of mesoscopic parameters into the macroscopic parameters of the liquid. Results include determining the distribution of the velocity field in the anastomosis area to modify its geometry. The study of the<br />influence of gravity on the nature of motion of fine-grained inclusions has been carried out. The quantitative characteristics of the delay<br />of particles in the area of anastomosis, depending on the dynamic viscosity of the liquid, are determined.<br />Conclusions. The three-dimensional mathematical model discussed in this paper is based on the application of the lattice Boltzmann<br />method for calculating the hydrodynamic parameters of the motion of fluid in the study area. The distinctive feature of the model is that<br />it accounts for the complex nature of the liquid having fine-grained inclusions. The model allows determining the behavior of these<br />inclusions and the field of speed with sufficient accuracy in real time. |
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Zaporizhzhya National Technical University 2018-05-29 13:24:17 |
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application/pdf http://ric.zntu.edu.ua/article/view/131559 |
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Radio Electronics, Computer Science, Control; No 1 (2018): Radio Electronics, Computer Science, Control |
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Copyright (c) 2018 M. A. Novotarskyi, S. G. Stirenko, Y. G. Gordienko |
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