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On 16th and 32th Order Multioperators-Based Schemes for Smooth and Discontinuous Fluid Dynamics Solutions

Part of: Shock waves and blast waves Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  21 June 2017

Andrei I. Tolstykh
Andrei I. Tolstykh*
Affiliation:
Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, 117999 Moscow GSP-1, Vavilova str. 40, Moscow Institute of Physics and Technology, Russia
*
*Corresponding author. Email address:tol@ccas.ru (A. I. Tolstykh)
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Abstract

The paper presents a novel family of arbitrary high order multioperators approximations for convection, convection-diffusion or the fluid dynamics equations. As particular cases, the 16th- and 32th-order skew-symmetric multioperators for derivatives supplied by the 15th- and 31th-order dissipation multioperators are described. Their spectral properties and the comparative efficiency of the related schemes in the case of smooth solutions are outlined. The ability of the constructed conservative schemes to deal with discontinuous solutions is investigated. Several types of nonlinear hybrid schemes are suggested and tested against benchmark problems.

Keywords

Arbitrary-order discretizationmultioperatorsequations with convection terms16th- and 32th-order schemesdiscontinuous solutions

MSC classification

Secondary: 65M06: Finite difference methods 65M99: None of the above, but in this section 76L05: Shock waves and blast waves 76L99: None of the above, but in this section
Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 2 , August 2017 , pp. 572 - 598
Copyright
Copyright © Global-Science Press 2017 

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Footnotes

Communicated by Chi-Wang Shu

References

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