On 16th and 32nd Order Multioperators-Based Schemes for Smooth and Discontinuous Fluid Dynamics Solutions (Communications in Computational Physics, 2018)
The paper presents a novel family of arbitrary high order multioperators approximationsfor convection, convection-diffusion or the fluid dynamics equations. Asparticular cases, the 16th- and 32nd-order skew-symmetric multioperators for derivativessupplied by the 15th- and 31st-order dissipation multioperators are described.Their spectral properties and the comparative efficiency of the related schemes in thecase of smooth solutions are outlined. The ability of the constructed conservativeschemes to deal with discontinuous solutions is investigated. Several types of nonlinearhybrid schemes are suggested and tested against benchmark problems.