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

  • Andrei I. TolstykhEmail author
Conference paper
Part of the Smart Innovation, Systems and Technologies book series (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.

Keywords

Multioperators Multioperators-based formulas Schemes for fluid dynamics Euler and Navier-Stokes equations Instability and sound radiation Discontinuous solutions 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Federal Research Center “Computer Science and Control” of the RASMoscowRussian Federation

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