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

Development of arbitrary-order multioperators-based schemes for parallel calculations.

“…In [8], one-parameter families of the Compact Upwind Differencing (CUD) operators from [2] were considered as multiplicative and additive corrections to three-point differencing operator DðsÞ ¼ ðD 0 À sD 2 Þ=2. Following the similar representation, it is possible to construct compact approximations which can be viewed as additive and multiplicative corrections to L h .…”

“…Thus it is advantageous, as in [8], to use the flux splitting The above described scheme requires switching from left to right operators or vice versa.…”

“…The extensions of the scheme to systems of conservation laws and multidimensional problems are outlined in [8]. In all cases, the Runge-Kutta time stepping or iterative procedures can be applied to form fully discretized schemes.…”

“…Comparing with the differencing multioperators described in [8], more parameters c i are needed to obtain a given approximation order resulting in larger values of the c coefficients. The sum and the difference of the multioperators are skew-symmetric and self-adjoint operators respectively, the latter being positive if D M;l is positive.…”

“…However, other types of multioperators (for example, central ones with artificially introduced free parameters) were also considered [7]. The brief outlines of the multioperators activity can be found in [8].…”