On 16th and 32th Order Multioperators-Based Schemes for Smooth and Discontinuous Fluid Dynamics Solutions. (21st June 2017)

• Record Type: Journal Article
• Authors: Tolstykh, Andrei I.
• Is Part Of: Communications in computational physics. Volume 22:Number 2(2017:Aug.)
• Page Start: 572
• Page End: 598
• Publication Date: 2017-06-21
• Subjects: 65M06, -- 65M99, -- 76L05, -- 76L99; Arbitrary-order discretization, -- multioperators, -- equations with convection terms, -- 16th- and 32th-order schemes, -- discontinuous solutions; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.141015.240217a
• Languages: English
• ISSNs: 1815-2406

Abstract

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.