MODELING OF LIQUID VORTICITY USING CELLULAR AUTOMATON

Authors

  • E. A. Nastenko National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute” Kyiv
  • A. V. Radahuz National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute” Kyiv

DOI:

https://doi.org/10.18372/1990-5548.54.12337

Keywords:

Cellular automata, derivation of hydrodynamics, molecular dynamics, hexagonal grid, Navier–Stokes equations

Abstract

A method has been developed for constructing large-scale electrophysiological models using extended cellular automata and for running such models on a cluster of shared memory systems. A method is proposed, including the extension of the language cellular automaton for the implementation of quantitative calculations, the construction of the whole-heart model with the Visible Human Project data, the parallelization of the model on a cluster of computers with a general and a simulation algorithm that connects the activity of cells with an electrocardiogram. It is shown that electrical activity at the level of canals, cells and organs can be traced in the extended system of cellular automata. Examples of some signals of electrocardiograms simulated by a two-dimensional cut are given. Also, an evaluation of the performance of a three-dimensional model on a four-member cluster.

Author Biographies

E. A. Nastenko, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute” Kyiv

Doctor of Biological Science. Professor.

Head of Department of biomedical cybernetics

A. V. Radahuz, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute” Kyiv

Post-graduate student

References

A. Gunstensen and D. Rothman, “Lattice Boltzmann model of immiscible fluids,” Physical Review, vol. 43, pp. 4320–4327, 1991.

U. Frisch, B. Hasslacher, and Y. Pomeau. “Lattice gas automata for the Navier–Stokes equation,” Physical Review, pp. 1505–1508, 1986.

S. Wolfram, “Cellular automata as models of complexity,” International weekly journal of science, pp. 471–526, 1984.

C. Boldea, “A Particle Cellular Automata Model for Fluid Simulations,” Math. Comp. Sci. Ser., vol. 36(2), pp. 35–41, 2009.

C. Hongsheng, Z. Zhong, C. Zhiwei, and T. Xiaotao, “A Lattice Gas Automata Model for the Coupled Heat Transfer and Chemical Reaction of Gas Flow Around and Through a Porous Circular Cylinder,” Entrophy, pp. 297–315, 2016.

S. Chen and Z. Wang, "Lattice Boltzmann computational fluid dynamics in three-dimensions," J. Stat. Phys, vol. 68, pp. 379–400, 1992.

S. Chen and W. Matthaeus, “Recovery of the Navier–Stokes equations using a lattice-gas Boltzmann method,” Physical Review A, 45(8), pp. 5339–5342, 1992.

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Issue

Vol. 4 No. 54 (2017)

Section

MATHEMATICAL MODELING OF PROCESSES AND SYSTEMS

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