APPLICATION OF R-FUNCTIONS METHOD AND SMOOTHED PARTICLE HYDRODYNAMICS FOR FLUID SIMULATION
Keywords:Navier-Stokes equations, fluid simulation, R-functions method, smoothed particle hydrodynamics, marching cubes algorithm
AbstractContext. 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.
Landau L. D., Lifshits E. M. Teoreticheskaya fizika. V 10 t. T. VI. Gidrodinamika. Moscow, Fizmatlit, 2003, 736 p.
Ladyizhenskaya O. A. Matematicheskie voprosyi dinamiki
vyazkoy neszhimaemoy zhidkosti. Moscow, Nauka, 1970, 288 p.
Rudman M., Cleary P. Using Smoothed particle hydrodynamics to study wave impact on floating offshore platforms,
Seventh International Conference on CFD in the Minerals and Process Industries, 2009, pp. 1–7.
Takahiro H. Seiichi K., Yoichiro K. Smoothed particle hydrodynamics in complex shapes, Proceedings of 23rd Spring
Conference on Computer Graphics, 2007, pp. 10–15.
Dai Z., Huang Y., Cheng H., Xu Q. 3D numerical modeling using smoothed particle hydrodynamics of flow-like landslide
propagation, Engineering Geology, 2014, Vol. 180, pp. 21–33. DOI: 10.1016/ j.enggeo.2014.03.018.
Barreiro A., Crespo A., Domínguez J. M., Gómez-Gesteira M. Smoothed Particle Hydrodynamics for coastal
engineering problems, Computers & Structures, 2013, V. 120, pp. 96–106. DOI: 10.1016/j.compstruc.2013.02.010.
Cleary P. W., Ha J. Three-dimensional smoothed particle hydrodynamics simulation of high pressure die casting of
light metal components, Journal of Light Metals, 2002,V. 2, No. 3, pp. 169–183. DOI: 10.1016/S1471-5317(02)00043-3.
Randles P., Libersky L. Smoothed Particle Hydrodynamics:Some recent improvements and applications, Computer
Methods in Applied Mechanics and Engineering, 1996, V. 139, No. 1–4, pp. 16–25. DOI: 10.1016/S0045-
Rvachev V. L. Ob analiticheskom opisanii nekotoryih geometricheskih ob’ektov, Dokl. AN SSSR, 1963, Vol. 153, № 4, pp. 765–768.
Rvachev V. L. Teoriya R-funktsiy i nekotoryie ee prilozheniya. Kyiv, Naukova dumka, 1982, 552 p.
Kravchenko V. F., Rvachev V. L. Algebra logiki, atomarnyie funktsii i veyvletyi v fizicheskih prilozheniyah. Moscow, Fizmatlit, 2006, 416 p.
Lorensen W., Cline H. Marching cubes: A high resolution 3D surface construction algorithm, Proceedings of the 14th annual conference on Computer graphics and interactive techniques (SIGGRAPH ‘87), 1987, pp. 163–169. DOI:10.1145/37401.37422.
Newman T. S. A survey of the marching cubes algorithm, Computers & Graphics, 2006, V. 30, No. 5, pp. 854–879.
DOI: 10.1016/ j.cag.2006.07.021.
Liu M. B., Liu G. R. Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments, Archives of
Computational Methods in Engineering, 2010, Vоl. 17, No. 1, pp. 25–76. DOI: 10.1007/s11831-010-9040-7.
Gomez-Gesteira M., Rogers B., Dalrymple R. A., Crespo A. State-of-the-art of classical SPH for free-surface flows,
Journal of Hydraulic Research, 2010, Vol. 48, pp. 6–27. DOI: 10.1080/00221686.2010.9641242.
Price D., Wurster J., Tricco T., Nixon C., Toupin S., Pettitt A. Phantom: A Smoothed Particle Hydrodynamics and Magnetohydrodynamics Code for Astrophysics, Publications of the Astronomical Society of Australia, 2018,
Vol. 35, pp. 10–35. DOI: 10.1017/pasa.2018.25.
Crespo A., Domínguez J. M. DualSPHysics: Open-source parallel CFD solver based on Smoothed Particle Hydrodynamics,
Computer Physics Communications, 2015, V. 187, pp. 204–216. DOI: 10.1016/j.cpc.2014.10.004.
Kelager M. Lagrangian fluid dynamics using smoothed particle hydrodynamics, University of Copenhagen, 2006, 88 p.
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