The Vector and Scalar Potential Method for the Numerical Solution of Two- and Three-Dimensional Navier-Stokes Equations
Abstract
A method is presented for the numerical finite-difference solution of the equations of motion for laminar, incompressible steady-state flow in both two and three dimensions. The complete Navier-Stokes 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 Navier-Stokes equations in a plane groove region. Numerical solutions of three-dimensional 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:
- 10.1016/0021-9991(77)90030-4
- Bibcode:
- 1977JCoPh..24..398A
- Keywords:
-
- Finite Difference Theory;
- Laminar Flow;
- Navier-Stokes 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