A parallel computational scheme with ninth-order multioperator approximations and its application to direct numerical simulation

Development of arbitrary-order multioperators-based schemes for parallel calculations. 1: Higher-than-fifth-order approximations to convection terms

“…The multioperators are based on another fifth-order operator from [2,7] (denoted here by L 5a ) and one of the third-order CUD basis operators from [2]. The table contains also the results of calculations with the fifth-order WENO scheme presented in [10]. As seen, the schemes with L 57 and L 59 outperform all other schemes demonstrating remarkably high accuracy (especially, in the latter case).…”

“…In Table 1, the results for L 57 , L 49 and L 59 multioperators corresponding to time t ¼ 0:3 are presented for several meshes with the number of nodes n. For comparison, the data from [10] obtained with the previous versions of ninth-order multioperators (denoted here by L 59a and L 39 ) are included in the table. The multioperators are based on another fifth-order operator from [2,7] (denoted here by L 5a ) and one of the third-order CUD basis operators from [2].…”

“…(9) and (10), one arrives at the fourth-order approximations to of =ox shown by the following Taylor expansion series:…”

“…The constructed approximations are applied in [8] to a finite-volume type of schemes for convection-diffusion equations and the Poisson equation. In the recent paper [10], the ninth-order multioperators with the CUD fifth-order basis operators from [7] were constructed. They were used for the direct numerical simulation of generation and decay of 2D turbulence in the case of a shear layer instability described by the incompressible Navier-Stokes equations.…”