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Multioperators Technique for Constructing Arbitrary High-Order Approximations and Schemes: Main Ideas and Applications to Fluid Dynamics Equations

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Smart Modeling for Engineering Systems (GCM50 2018)

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 133))

Abstract

The main ideas of multioperators as tools for constructing arbitrary high-order approximations and schemes are outlined. Examples of multioperators-based numerical analysis formulas are presented. Schemes for fluid dynamics with multioperators approximations up to 36th-order are described. Numerical results of high fidelity long term calculations for instability and sound radiation problems are presented. The extension to strongly discontinuous solutions is briefly outlined.

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References

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Authors and Affiliations

  1. Federal Research Center “Computer Science and Control” of the RAS, 40 Vavilova ul., 119333, Moscow, Russian Federation

    Andrei I. Tolstykh

Authors
  1. Andrei I. Tolstykh
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Correspondence to Andrei I. Tolstykh .

Editor information

Editors and Affiliations

  1. Department of Computer Science and Numerical Mathematics, Moscow Institute of Physics and Technology, Dolgoprudny, The Moscow Area, Russia

    Igor B. Petrov

  2. Department of Applied Computational Geophysics, Moscow Institute of Physics and Technology, Dolgoprudny, The Moscow Area, Russia

    Alena V. Favorskaya

  3. Institute of Informatics and Telecommunications, Reshetnev Siberian State University of Science and Technology, Krasnoyarsk, Russia

    Margarita N. Favorskaya

  4. Department of Computational Physics, Moscow Institute of Physics and Technology, Dolgoprudny, The Moscow Area, Russia

    Sergey S. Simakov

  5. Faculty of Engineering and Information Technology, Centre for Artificial Intelligence, University of Technology, Sydney, NSW, Australia

    Lakhmi C. Jain

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Tolstykh, A.I. (2019). Multioperators Technique for Constructing Arbitrary High-Order Approximations and Schemes: Main Ideas and Applications to Fluid Dynamics Equations. In: Petrov, I., Favorskaya, A., Favorskaya, M., Simakov, S., Jain, L. (eds) Smart Modeling for Engineering Systems. GCM50 2018. Smart Innovation, Systems and Technologies, vol 133. Springer, Cham. https://doi.org/10.1007/978-3-030-06228-6_3

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