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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2018, Volume 58, Number 4, Pages 530–540
DOI: https://doi.org/10.7868/S004446691804004X
(Mi zvmmf10716)
 

This article is cited in 7 scientific papers (total in 7 papers)

Asymptotic expansion of Crocco solution and the Blasius constant

V. P. Varin

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia
Citations (7)
References:
Abstract: We consider the Crocco equation (the reduction of the Blasius equation). The use of this more simple equation for computation of the Blasius constant leads to some unexpected difficulties, which have been unexplained. We computed the asymptotic expansion of the solution to Crocco equation at its singularity. This expansion was unknown before. We describe the structure of the Riemann surface of the Crocco solution at the singularity. These results were used for construction of an effective numerical algorithm, which is based on analytical continuation, for computation of the Blasius constant with an arbitrary and guaranteed accuracy. We computed the Blasius constant with a 100 decimal places.
Key words: Crocco equation, Blasius constant, asymptotic expansion, analytical continuation.
Received: 06.03.2017
Revised: 10.08.2017
English version:
Computational Mathematics and Mathematical Physics, 2018, Volume 58, Issue 4, Pages 517–528
DOI: https://doi.org/10.1134/S0965542518040164
Bibliographic databases:
Document Type: Article
UDC: 516.62
Language: Russian
Citation: V. P. Varin, “Asymptotic expansion of Crocco solution and the Blasius constant”, Zh. Vychisl. Mat. Mat. Fiz., 58:4 (2018), 530–540; Comput. Math. Math. Phys., 58:4 (2018), 517–528
Citation in format AMSBIB
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Linking options:
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  • https://www.mathnet.ru/eng/zvmmf/v58/i4/p530
  • This publication is cited in the following 7 articles:
    1. Victor Petrovich Varin, “Localazation of movable singularities of the Blasius equation”, KIAM Prepr., 2024, no. 83, 1  crossref
    2. J. Majdalani, L.-J. Xuan, “On the Karman momentum-integral approach and the Pohlhausen paradox”, Phys. Fluids, 32:12 (2020), 123605  crossref  adsnasa  isi
    3. V. P. Varin, “Nonlocal singularities on families of periodic solutions to ordinary differential equations”, Comput. Math. Math. Phys., 60:1 (2020), 53–64  mathnet  crossref  crossref  isi  elib
    4. V. N. Laptinskii, “Exact solution of the prandtl problem about a dynamic laminar boundary layer”, Differ. Equ., 56:4 (2020), 538–542  crossref  mathscinet  zmath  isi
    5. M. R. Petrichenko, V E. Kotov, “Numerical verification of weak solutions of the Crocco typical boundary problem using an implicit second order difference scheme”, St. Petersb. Polytech. Univ. J.-Phys. Math., 12:2 (2019), 63–72  crossref  isi
    6. S. V. Pikulin, “The Thomas–Fermi problem and solutions of the Emden–Fowler equation”, Comput. Math. Math. Phys., 59:8 (2019), 1292–1313  mathnet  mathnet  crossref  crossref  isi  scopus
    7. Mikhail Petrichenko, Vitaly Sergeev, Evgeny Kotov, Darya Nemova, Darya Tarasova, Advances in Intelligent Systems and Computing, 983, International Scientific Conference Energy Management of Municipal Facilities and Sustainable Energy Technologies EMMFT 2018, 2019, 839  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    References:45
     
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