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7Methods of computational algebra and solving mathematical physics equations
References
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Smoothed particle hydrodynamics methodfor numericalsolution of filtering problems
of three.phases fluid
V. V. Bashurov
FSUE �Russian Federal Nuclear Center�All.Russian Research Institute of Experimental Physics�, Sarov, Nizhny
Novgorod Region
Email: bashurov@mail.ru
DOI 10.24412/cl.35065.2021.1.00.99
This work is devoted to solving the problem of filtration of a mixture of water, gas and oil in a homogeneous
porous medium.The basic equations of filtration theory [1] are converted into a special form for numerical
approximation by the smoothed particle method. A numerical difference scheme is constructed on the basis of
the smoothed particle hydrodynamics method [2]. An algorithm for setting the boundary conditions is proposed
and a number of isothermal one.dimensional and two.dimensional test numerical calculations of the
filtration process of a mixture of water, oil and gas are presented.
References
1. Parker J.C., Lenhard R., Kuppusami T. A parametric model for constitutive properties governing multiphase flow in
porous media.�.Water Resources Research. 1987. V. 23, no.4. p. 618�624.
2. Gingold R.A., Monaghan J.J. Smoothed particle hydrodynamics: theory and application to non.spherical stars.
Mon. Not. Roy.Astron. Soc. 1977.375 p.
The least.squares collocation method and its applications to problems of continuum mechanics
V. A. Belyaev1
1Khristianovich Institute of Theoreticaland Applied Mechanics SB RAS
Email: belyaevasily@mail.ru
DOI 10.24412/cl.35065.2021.1.00.03
The report is devoted to an application of the developed versions of the least.squares collocation (LSC)
method to solving continuum mechanic problems. The efficiency of their combination with various methods of
acceleratingiterative processes is shown. Possibilities of the LSC method for solving boundary value problems
for differentialequations of various orders in canonical and irregular domains, including those with singularities,
are investigated [1]. Mathematicalmodelling and numerical simulation of composite beam bending, calculation
of thin plates bending, and numerical analysis of polymer fluid flows are carried out. Comparison with
the results of other authors shows the advantages of the LSѠmethod, as well as satisfactory agreement with
experimental data in calculations.
