Application of an implicit timemarching scheme to a threedimensional incompressible flow problem in curvilinear coordinate systems
Abstract
An implicit finitedifference scheme based on the SMAC method for solving steady threedimensional incompressible viscous flows is proposed. The threedimensional incompressible NavierStokes equations in general curvilinear coordinates, in which the contravariant velocities and the pressure are used as the unknown variables, have been derived by the authors. The momentum equations for the contravariant velocity components and the elliptic equation for the pressure are solved directly in the transformed space by applying the deltaform approximatefactorization scheme and the Tschebyscheff SLOR method, respectively. The present implicit scheme is stable under correctly imposed boundary conditions, since the spurious error and the numerical instabilities can be suppressed by satisfying the continuity condition identically, and by employing the staggered grid and the TVD upwind scheme. Some numerical results for threedimensional flow over a backwardfacing step are shown to demonstrate the reliability of the present scheme and to clarify the threedimensional effects of such complex flows.
 Publication:

Computers and Fluids
 Pub Date:
 April 1992
 Bibcode:
 1992CF.....21..163I
 Keywords:

 Computational Fluid Dynamics;
 Incompressible Flow;
 Spherical Coordinates;
 Three Dimensional Flow;
 Time Marching;
 Finite Difference Theory;
 NavierStokes Equation;
 Steady Flow;
 Viscous Flow;
 Fluid Mechanics and Heat Transfer