COMPACT FINITE DIFFERENCE-FOURIER SPECTRAL METHOD FOR THREE-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

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