• A. V. Artiukh Kharkiv National University of Radio Electronics, Kharkiv
  • S. I. Kozyrenko Kharkiv National University of Radio Electronics, Kharkiv
  • O. O. Shabalin Kharkiv National University of Radio Electronics, Kharkiv
  • I. R. Lytvyn Kharkiv National University of Radio Electronics, Kharkiv



Navier-Stokes equations, fluid simulation, R-functions method, smoothed particle hydrodynamics, marching cubes algorithm


Context. Existing fluid simulation methods have several disadvantages and can be improved with the help of new approaches to
the solution of problems of computational fluid dynamics, which confirms the relevance of the work.
Objective. The goal of the work is to improve existing methods of mathematical modeling of fluid based on smoothed particle
hydrodynamics and R-functions method.
Method. A new approach of joint use of smoothed particle hydrodynamics, marching cubes and R-functions method is proposed.
Smoothed particle hydrodynamics helps to simulate fluid movement in real time. The method considers fluid as a discrete number of
sample points (particles), which have mass, velocity, position and physical field quantities (pressure, temperature, mass-density, etc.).
The R-functions method allows to solve the inverse problem of analytic geometry: finding an analytical equation of a 2D (3D) object
based on its geometrical representation. Using the obtained equation, one can simply detect a particle collision with the object
boundary and plot the object surface with the help of marching cubes algorithm. The suggested method allows to achieve good simulation
quality and to perform all needed calculations and rendering in real time.
Results. Computational experiments for the problem of fluid simulation were carried out. Various numbers of particles were
used. Different kinds of objects were put into the considered region in order to investigate the fluid behavior.
Conclusions. The results of visual simulations allow us to say that the obtained approach works as expected. Therefore, this
method can be applied to several problems of fluid simulation where the collision detection with arbitrary objects is considered. Further
research may be devoted to the optimization of neighbor-search algorithm, to performing all calculations in graphics processing
unit or to taking into account other physical quantities.

Author Biographies

A. V. Artiukh, Kharkiv National University of Radio Electronics, Kharkiv

PhD, Associate Professor of the Department of Applied Mathematics

S. I. Kozyrenko, Kharkiv National University of Radio Electronics, Kharkiv

PhD, Associate Professor, Associate Professor of the Department of Applied Mathematics

O. O. Shabalin, Kharkiv National University of Radio Electronics, Kharkiv

Researcher of the Department of Applied Mathematics

I. R. Lytvyn, Kharkiv National University of Radio Electronics, Kharkiv

Student of the Department of Applied Mathematics


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How to Cite

Artiukh, A. V., Kozyrenko, S. I., Shabalin, O. O., & Lytvyn, I. R. (2019). APPLICATION OF R-FUNCTIONS METHOD AND SMOOTHED PARTICLE HYDRODYNAMICS FOR FLUID SIMULATION. Radio Electronics, Computer Science, Control, (3), 25–33.



Mathematical and computer modelling