A solution method for the unsteady incompressible NavierStokes equations in generalized coordinate systems
Abstract
A solution method based on a fractional step approach is developed for obtaining timedependent solutions of the threedimensional, incompressible NavierStokes equations in generalized coordinate systems. The governing equations are discretized conservatively by finite volumes using a staggered mesh system. The primitive variable formulation uses the volume fluxes across the faces of each computational cell as dependent variables. This procedure, combined with accurate and consistent approximations of geometric parameters, is done to satisfy the discretized mass conservation equation to machine accuracy as well as to gain favorable convergence properties of the Poisson solver. The discretized equations are secondorderaccurate in time and space and no smoothing terms are added. An approximatefactorization scheme is implemented in solving the momentum equations. A novel ZEBRA scheme with fourcolor ordering is devised for the efficient solution of the Poisson equation. Several two and threedimensional solutions are compared with other numerical and experimental results to validate the present method.
 Publication:

26th AIAA Aerospace Sciences Meeting
 Pub Date:
 January 1988
 Bibcode:
 1988aiaa.meetZ....R
 Keywords:

 Computational Fluid Dynamics;
 Incompressible Flow;
 NavierStokes Equation;
 Unsteady Flow;
 Cavitation Flow;
 Circular Cylinders;
 Conservation Equations;
 Numerical Flow Visualization;
 Poisson Equation;
 Three Dimensional Flow;
 Viscous Flow;
 Fluid Mechanics and Heat Transfer