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Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 3, Pages 557–562 (Mi zvmmf4851)  

This article is cited in 3 scientific papers (total in 3 papers)

Regularization of a discrete scheme for a three-dimensional problem of the evolution of the interface of different fluids

D. N. Nikol'skiĭ

Orel State University, Komsomol'skaya ul. 95, Orel, 302015 Russia

Abstract: A regularized discrete scheme is developed that describes the three-dimensional evolution of the interface between fluids with different viscosities and densities in the Leibenzon–Muskat model. The regularization is achieved by smoothing the kernel of the singular integral involved in the differential equation governing the moving interface. The discrete scheme is tested by solving the problem of a drop of one fluid evolving in a translational flow of another.

Key words: three-dimensional evolution of a fluid-fluid interface, regularization of a discrete scheme, smoothing of the kernel of a singular integral.

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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:3, 531–536

Bibliographic databases:

UDC: 519.634
Received: 15.09.2009

Citation: D. N. Nikol'skiǐ, “Regularization of a discrete scheme for a three-dimensional problem of the evolution of the interface of different fluids”, Zh. Vychisl. Mat. Mat. Fiz., 50:3 (2010), 557–562; Comput. Math. Math. Phys., 50:3 (2010), 531–536

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Nikolskii D.N., “Matematicheskoe modelirovanie ploskikh filtratsionnykh techenii v oblastyakh s granitsami i polupronitsaemymi vklyucheniyami”, Uchenye zapiski Orlovskogo gos. un-ta. Ser.: Estestvennye, tekhnicheskie i meditsinskie nauki, 2010, no. 4, 7–11  elib
    2. D. N. Nikol'skii, “Three-dimensional evolution of the boundary of a polluted area in a bounded piecewise homogeneous porous material”, Comput. Math. Math. Phys., 51:5 (2011), 855–861  mathnet  crossref  mathscinet  isi
    3. Nesterenko D.S., “O povyshenii ustoichivosti prostranstvennykh zadach evolyutsii granitsy razdela zhidkostei razlichnoi plotnosti i vyazkosti putem vosstanovleniya ee ravnomernogo predstavleniya”, Uchenye zapiski Orlovskogo gosudarstvennogo universiteta. Seriya: Estestvennye, tekhnicheskie i meditsinskie nauki, 2013, no. 6, 54–58  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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