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Computer Research and Modeling, 2021, Volume 13, Issue 5, Pages 979–992
DOI: https://doi.org/10.20537/2076-7633-2021-13-5-979-992
(Mi crm929)
 

This article is cited in 2 scientific papers (total in 2 papers)

NUMERICAL METHODS AND THE BASIS FOR THEIR APPLICATION

The two geometric parameters influence study on the hydrostatic problem solution accuracy by the SPH method

I. I. Potapov, O. V. Reshetnikova

Computing Center of the Far Eastern Branch of the Russian Academy of Sciences, 65 Kim U Chena st., Khabarovsk, 680000, Russia
Full-text PDF (395 kB) Citations (2)
References:
Abstract: The two significant geometric parameters are proposed that affect the physical quantities interpolation in the smoothed particle hydrodynamics method (SPH). They are: the smoothing coefficient which the particle size and the smoothing radius are connecting and the volume coefficient which determine correctly the particle mass for a given particles distribution in the medium.
In paper proposes a technique for these parameters influence assessing on the SPH method interpolations accuracy when the hydrostatic problem solving. The analytical functions of the relative error for the density and pressure gradient in the medium are introduced for the accuracy estimate. The relative error functions are dependent on the smoothing factor and the volume factor. Designating a specific interpolation form in SPH method allows the differential form of the relative error functions to the algebraic polynomial form converting.The root of this polynomial gives the smoothing coefficient values that provide the minimum interpolation error for an assigned volume coefficient.
In this work, the derivation and analysis of density and pressure gradient relative errors functions on a sample of popular nuclei with different smoothing radius was carried out. There is no common the smoothing coefficient value for all the considered kernels that provides the minimum error for both SPH interpolations. The nuclei representatives with different smoothing radius are identified which make it possible the smallest errors of SPH interpolations to provide when the hydrostatic problem solving. As well, certain kernels with different smoothing radius was determined which correct interpolation do not allow provide when the hydrostatic problem solving by the SPH method.
Keywords: incompressible medium motion, SPH, smoothed particle hydrodynamic, kernel, smoothing radius, interpolation function, value reproduction accuracy, conservation laws.
Funding agency Grant number
Russian Foundation for Basic Research 18-05-00530
The work was supported by grant of RFBR № 18-05-00530 А.
Received: 17.06.2021
Revised: 19.08.2021
Accepted: 23.08.2021
Document Type: Article
UDC: 532.545
Language: Russian
Citation: I. I. Potapov, O. V. Reshetnikova, “The two geometric parameters influence study on the hydrostatic problem solution accuracy by the SPH method”, Computer Research and Modeling, 13:5 (2021), 979–992
Citation in format AMSBIB
\Bibitem{PotRes21}
\by I.~I.~Potapov, O.~V.~Reshetnikova
\paper The two geometric parameters influence study on the hydrostatic problem solution accuracy by the SPH method
\jour Computer Research and Modeling
\yr 2021
\vol 13
\issue 5
\pages 979--992
\mathnet{http://mi.mathnet.ru/crm929}
\crossref{https://doi.org/10.20537/2076-7633-2021-13-5-979-992}
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  • https://www.mathnet.ru/eng/crm929
  • https://www.mathnet.ru/eng/crm/v13/i5/p979
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Computer Research and Modeling
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    Abstract page:90
    Full-text PDF :33
    References:22
     
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