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Volume 22, Issue 2
On 16th and 32nd Order Multioperators-Based Schemes for Smooth and Discontinuous Fluid Dynamics Solutions

Andrei I. Tolstykh

DOI: 10.4208/cicp.141015.240217a

Commun. Comput. Phys., 22 (2017), pp. 572-598.

Published online: 2018-04

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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 32nd-order skew-symmetric multioperators for derivatives supplied by the 15th- and 31st-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.

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@Article{CiCP-22-572, author = {Andrei I. Tolstykh}, title = {On 16th and 32nd Order Multioperators-Based Schemes for Smooth and Discontinuous Fluid Dynamics Solutions}, journal = {Communications in Computational Physics}, year = {2018}, volume = {22}, number = {2}, pages = {572--598}, 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 32nd-order skew-symmetric multioperators for derivatives supplied by the 15th- and 31st-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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.141015.240217a}, url = {http://global-sci.org/intro/article_detail/cicp/11311.html} }
TY - JOUR T1 - On 16th and 32nd Order Multioperators-Based Schemes for Smooth and Discontinuous Fluid Dynamics Solutions AU - Andrei I. Tolstykh JO - Communications in Computational Physics VL - 2 SP - 572 EP - 598 PY - 2018 DA - 2018/04 SN - 22 DO - http://doi.org/10.4208/cicp.141015.240217a UR - https://global-sci.org/intro/article_detail/cicp/11311.html KW - AB -

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 32nd-order skew-symmetric multioperators for derivatives supplied by the 15th- and 31st-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.

Andrei I. Tolstykh. (2018). On 16th and 32nd Order Multioperators-Based Schemes for Smooth and Discontinuous Fluid Dynamics Solutions. Communications in Computational Physics. 22 (2). 572-598. doi:10.4208/cicp.141015.240217a
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