A solution procedure for incompressible Navier-Stokes equations
A solution procedure, suitable for finite difference implementations, was developed for the solution of the three-dimensional, unsteady, incompressible Navier-Stokes equations written in primitive variables. The procedure is based on the idea of satisfying the continuity equation directly and explicitly at all times, and letting the pressure gradient develop as a consequence of the velocity variation compliant with the specified boundary conditions. This is in contrast with the conventional approach to the set of equations constituting the incompressible Navier-Stokes equations, in which the continuity equation is regarded as a constraint to be satisfied by the velocity components whose correct values should be found by adjusting the pressure gradient. A simple finite difference method, based on the present solution procedures, was applied to the problem of a square driven cavity. The steady state solution for Reynolds number of 100, which serves as a standard test case for comparison of numerical methods for incompressible Navier-Stokes equations, is in good agreement with existing numerical solutions. Overall, the solution provides a simple and practical means of computing general three-dimensional unsteady fluid flows which are governed by the incompressible Navier-Stokes equations.
- Research Organization:
- Texas Univ., Arlington, TX (USA)
- OSTI ID:
- 5172115
- Country of Publication:
- United States
- Language:
- English
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