A Fractional Step Solution Method for the Unsteady Incompressible NavierStokes Equations in Generalized Coordinate Systems
Abstract
A fractional step method is developed for solving the timedependent threedimensional incompressible NavierStokes equations in generalized coordinate systems. The primitive variable formulation uses the pressure, defined at the center of the computational cell, and the volume fluxes across the faces of the cells as the dependent variables, instead of the Cartesian components of the velocity. This choice is equivalent to using the contravariant velocity components in a staggered grid multiplied by the volume of the computational cell. The governing equations are discretized by finite volumes using a staggered mesh system. The solution of the continuity equation is decoupled from the momentum equations by a fractional step method which enforces mass conservation by solving a Poisson equation. This procedure, combined with a consistent approximation of the geometric quantities, is done to satisfy the discretized mass conservation equation to machine accuracy, as well as to gain the favorable convergence properties of the Poisson solver. The momentum equations are solved by an approximate factorization method, and a novel ZEBRA scheme with fourcolor ordering is devised for the efficient solution of the Poisson equation. Several two and threedimensional laminar test cases are computed and compared with other numerical and experimental results to validate the solution method. Good agreement is obtained in all cases.
 Publication:

Journal of Computational Physics
 Pub Date:
 May 1991
 DOI:
 10.1016/00219991(91)90139C
 Bibcode:
 1991JCoPh..94..102R
 Keywords:

 Computational Fluid Dynamics;
 Incompressible Flow;
 NavierStokes Equation;
 Newtonian Fluids;
 Three Dimensional Flow;
 Unsteady Flow;
 Cartesian Coordinates;
 Circular Cylinders;
 Ducted Flow;
 Finite Volume Method;
 Poisson Equation;
 Reynolds Number;
 Viscous Flow;
 Fluid Mechanics and Heat Transfer