Fifth- and seventh-order accurate multioperator compact schemes

The properties of fifth- and seventh-order accurate multioperator compact schemes based on well-known third- and fifth-order accurate compact approximations are investigated. The region where the multioperators have definite signs is determined numerically. A comparison is given with the exact solutions of the stationary Burgers equation and the problem of vortex convection by a compressible inviscid gas flow. An application of multioperator schemes to a viscous compressible gas flow in the stator of a turbine is considered.