SIMULATION OF 3D TRANSIENT FLOW PASSING THROUGH AN INTESTINAL ANASTOMOSIS BY LATTICE-BOLTZMANN METHOD

Authors

  • M. A. Novotarskyi National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine, Ukraine
  • S. G. Stirenko National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine, Ukraine
  • Y. G. Gordienko National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine, Ukraine

DOI:

https://doi.org/10.15588/1607-3274-2018-1-9

Keywords:

mathematical model, lattice method of Boltzmann, anastomosis simulation

Abstract

Context. Recently, the number of reconstructive operations on the digestive tract has significantly increased. Such operations have
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.
Objective. The purpose of the work is to develop a three-dimensional mathematical model of anastomosis for research of hydrodynamic
parameters of fluids with complex structure in real time.
Method. The method of constructing and analyzing the mathematical model of anastomosis of the digestive tract based on lattice
Boltzmann method is proposed. The method differs in that it provides simultaneous analysis of hydrodynamic parameters of the liquid and
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
influence of gravity on the nature of motion of fine-grained inclusions has been carried out. The quantitative characteristics of the delay
of particles in the area of anastomosis, depending on the dynamic viscosity of the liquid, are determined.
Conclusions. The three-dimensional mathematical model discussed in this paper is based on the application of the lattice Boltzmann
method for calculating the hydrodynamic parameters of the motion of fluid in the study area. The distinctive feature of the model is that
it accounts for the complex nature of the liquid having fine-grained inclusions. The model allows determining the behavior of these
inclusions and the field of speed with sufficient accuracy in real time.

References

Nesterenko B. B. Mathematical simulation for parallel

asynchronous methods of boundary value problems of

mathematical physics / B. B. Nesterenko, M. A. Novotarskiy //

IMACS World Congress: 16th international conference, Lausanne, 21–25 August 2000: proceedings. – Ecole Polytechnique Federale de Louzanne, 2000. – P. 116–122. 2. Rosenau Ph. Extending hydrodynamics via the regularization of the Chapman-Enskog expansion / Ph. Rosenau // Physical Review A. – 1989. – Vol. 40, Issue 12. – P. 7193–7196. DOI: 10.1103/PhysRevA.40.7193.

Temam R. Navier-stokes equations: theory and numerical analysis/ R. Temam. – Amsterdam: North-Holland, 1984. – 408 p.

Mitchell A. R. The finite difference method in partial differential equations / A. R. Mitchell, D. F. Griffiths. – New York: John Wiley, 1980. – 272 p.

Girault V. Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms / V. Girault, P-A. Rivart. – Berlin: Springer-Verlag, 1980. – 375 p. DOI: 10.1007/978-3-642-61623 5.

Versteeg H. K. An Introduction to Computational Fluid Dynamics: The Finite Volume Method / H. K. Versteeg, M. Malalasekera. – London: Paerson education Ltd., 1995. – 511 p.

Vilsmeier R. Finite volumes for complex applications II: problems and perspectives / R. Vilsmeier, F. Benkhaldoun, D. H nel. – Middlesex: Hermes Science Publications, 1999. – 887 p.

Chen S. Lattice Boltzmann method for fluid flows / S. Chen,

G. Doolen // Annual Review of Fluid Mechanics. – 1998. –

Vol. 30. – P. 329–364. DOI: 10.1146/annurev.fluid.30.1.329.

Jahanshaloo L. An overview of boundary implementation in

lattice Boltzmann method for computational heat and mass

transfer / L. Jahanshaloo, N. A. C. Sidik, A. Fazeli // International Communications in Heat and Mass Transfer. – 2016. – Vol. 78, Issue 11. – P. 1–12. DOI: 10.1016/

j.icheatmasstransfer.2016.08.014.

Tan J. A parallel fluid solid coupling model using LAMMPS and Palabos based on the immersed boundary method / J. Tan, T. Sinno, S. Diamond, [Electronic resource]. – https://arxiv.org/abs/1704.04551.

Downloads

How to Cite

Novotarskyi, M. A., Stirenko, S. G., & Gordienko, Y. G. (2018). SIMULATION OF 3D TRANSIENT FLOW PASSING THROUGH AN INTESTINAL ANASTOMOSIS BY LATTICE-BOLTZMANN METHOD. Radio Electronics, Computer Science, Control, (1), 75–82. https://doi.org/10.15588/1607-3274-2018-1-9

Issue

No. 1 (2018): Radio Electronics, Computer Science, Control

Section

Mathematical and computer modelling

License

Copyright (c) 2018 M. A. Novotarskyi, S. G. Stirenko, Y. G. Gordienko

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Creative Commons Licensing Notifications in the Copyright Notices

The journal allows the authors to hold the copyright without restrictions and to retain publishing rights without restrictions.

The journal allows readers to read, download, copy, distribute, print, search, or link to the full texts of its articles.

The journal allows to reuse and remixing of its content, in accordance with a Creative Commons license СС BY -SA.

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License CC BY-SA that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.

  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.

  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.