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Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 8, Pages 1433–1452 (Mi zvmmf429)  

This article is cited in 13 scientific papers (total in 13 papers)

A parallel computational scheme with ninth-order multioperator approximations and its application to direct numerical simulation

M. V. Lipavskii, A. I. Tolstykh, E. N. Chigerëv

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia

Abstract: The properties of ninth-order multioperator compact schemes based on known third-and fifth-order compact approximations are examined. The domains where the multioperators have fixed signs are determined numerically. The numerical results are compared with the exact solution to the Burgers equation. The multioperator schemes are applied to the problem of vortex sheet roll-up.

Key words: multioperator approximations, direct numerical simulation problems, parallel computations, compact upwind approximations.

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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:8, 1359–1377

Bibliographic databases:

UDC: 519.63
Received: 29.12.2005

Citation: M. V. Lipavskii, A. I. Tolstykh, E. N. Chigerëv, “A parallel computational scheme with ninth-order multioperator approximations and its application to direct numerical simulation”, Zh. Vychisl. Mat. Mat. Fiz., 46:8 (2006), 1433–1452; Comput. Math. Math. Phys., 46:8 (2006), 1359–1377

Citation in format AMSBIB
\by M.~V.~Lipavskii, A.~I.~Tolstykh, E.~N.~Chiger\"ev
\paper A~parallel computational scheme with ninth-order multioperator approximations and its application to direct numerical simulation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 8
\pages 1433--1452
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 8
\pages 1359--1377

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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. Tolstykh A.I., “Development of arbitrary-order multioperators-based schemes for parallel calculations. I. Higher-than-fifth-order approximations to convection terms”, J. Comput. Phys., 225:2 (2007), 2333–2353  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Tolstykh A.I., Lipavskii M.V., Savel'ev A.D., Shirobokov D.A., “Highly accurate multioperators schemes for aeroacoustics with application to noise generated by jets”, Proceedings of Isma 2008: International Conference on Noise and Vibration Engineering, 2008, 549–563  isi
    3. A. D. Savel'ev, A. I. Tolstykh, D. A. Shirobokov, “Application of compact and multioperator schemes to the numerical simulation of acoustic fields generated by instability waves in supersonic jets”, Comput. Math. Math. Phys., 49:7 (2009), 1221–1234  mathnet  crossref  isi
    4. A. D. Savel'ev, “On the structure of internal dissipation of composite compact schemes for gasdynamic simulation”, Comput. Math. Math. Phys., 49:12 (2009), 2135–2148  mathnet  crossref  isi
    5. A. I. Tolstykh, “On families of compact fourth- and fifth-order approximations involving the inversion of two-point operators for equations with convective terms”, Comput. Math. Math. Phys., 50:5 (2010), 848–861  mathnet  crossref  adsnasa  isi
    6. A. I. Tolstykh, “On the multioperator method for constructing approximations and finite difference schemes of an arbitrarily high order”, Comput. Math. Math. Phys., 51:1 (2011), 51–67  mathnet  crossref  mathscinet  isi
    7. Lipavskii M.V., Savelev A.D., Tolstykh A.I., Shirobokov D.A., “Multioperatornye skhemy do 18-go poryadka tochnosti s prilozheniyami k zadacham neustoichivosti i akustiki strui”, Uchenye zapiski TsAGI, 43:3 (2012), 16–33  elib
    8. Kostin V.I., “Raschet techenii vyazkoi neszhimaemoi zhidkosti s pomoschyu skhem povyshennoi tochnosti”, Nauchnyi vestnik moskovskogo gosudarstvennogo tekhnicheskogo universiteta grazhdanskoi aviatsii, 2012, no. 184, 62–71  elib
    9. M. V. Lipavskii, A. I. Tolstykh, “Tenth-order accurate multioperator scheme and its application in direct numerical simulation”, Comput. Math. Math. Phys., 53:4 (2013), 455–468  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    10. M. V. Lipavskii, A. I. Tolstykh, E. N. Chigerev, “Numerical simulation of shear layer instability using a scheme with ninth-order multioperator approximations”, Comput. Math. Math. Phys., 53:3 (2013), 296–310  mathnet  crossref  crossref  mathscinet  zmath  elib  elib
    11. A. I. Tolstykh, “Hybrid schemes with high-order multioperators for computing discontinuous solutions”, Comput. Math. Math. Phys., 53:9 (2013), 1303–1322  mathnet  crossref  crossref  isi  elib  elib
    12. O. A. Azarova, “Complex conservative difference schemes for computing supersonic flows past simple aerodynamic forms”, Comput. Math. Math. Phys., 55:12 (2015), 2025–2049  mathnet  crossref  crossref  mathscinet  isi  elib
    13. A. I. Tolstykh, “On the use of multioperators in the construction of high-order grid approximations”, Comput. Math. Math. Phys., 56:6 (2016), 932–946  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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