Compact finite difference - Fourier spectral method for three-dimensional incompressible Navier-Stokes equations

A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth-order center compact schemes for the derivatives in spectral space are described, respectively. The fourth-order compact schemes in a single nine-point cell for solving the Helmholtz equations satisfied by the velocities and pressure in spectral space is derived and its preconditioned conjugate gradient iteration method is studied. The treatment of pressure boundary conditions and the three dimensional non-reflecting outflow boundary conditions are presented. Application to the vortex dislocation evolution in a three dimensional wake is also reported.

Spectral-line profile of turbulent gas

phases should be specified when the particle Reynolds number is higher than

How much efficiency gains and price reductions for an efficiency defense? 'Quanto Basta'

Potential efficiency gains due to a merger can be used by competition authorities to judge upon proposed mergers. In a world where agents’ efforts, observable or unobservable, affect the success of a production cost reducing project that may be conducted as a stand-alone firm or in a merger, we characterize the merger decision and the type of errors a competition authority may make when it relies on an efficiency defense. In addition, we show that the occurrence of either type of errors is always smaller under the unobservable efforts assumption, than under the observable efforts one.