The Vector and Scalar Potential Method for the Numerical Solution of Two and ThreeDimensional NavierStokes Equations
Abstract
A method is presented for the numerical finitedifference solution of the equations of motion for laminar, incompressible steadystate flow in both two and three dimensions. The complete NavierStokes equations are transformed and expressed in terms of vorticity, scalar, and vector potentials. The transformed equations are solved iteratively. The method is evaluated by solving the NavierStokes equations in a plane groove region. Numerical solutions of threedimensional flows in a square duct and in a rectangular cavity formed in one wall of a square duct are presented. The results obtained are compared with the experimental results and other calculations.
 Publication:

Journal of Computational Physics
 Pub Date:
 August 1977
 DOI:
 10.1016/00219991(77)900304
 Bibcode:
 1977JCoPh..24..398A
 Keywords:

 Finite Difference Theory;
 Laminar Flow;
 NavierStokes Equation;
 Steady Flow;
 Three Dimensional Flow;
 Two Dimensional Flow;
 Cavities;
 Ducted Flow;
 Equations Of Motion;
 Incompressible Flow;
 Iterative Solution;
 Vorticity;
 Fluid Mechanics and Heat Transfer