# Accession Number:

## ADA149851

# Title:

## Solution of the Three-Dimensional Navier-Stokes Equations for a Steady Laminar Horseshoe Vortex Flow.

# Descriptive Note:

## Final rept. 1 Jun 82-30 Jun 84,

# Corporate Author:

## SCIENTIFIC RESEARCH ASSOCIATES INC GLASTONBURY CT

# Personal Author(s):

# Report Date:

## 1984-12-01

# Pagination or Media Count:

## 43.0

# Abstract:

A low Mach number formulation of the three-dimensional Navier-Stokes equations is solved for a steady laminar horseshoe vortex flow, using a time-iterative approach. A split linearized block implicit algorithm is used, with central spatial differences in a transformed coordinate system. The stability of this algorithm in three dimensions is examined for a scalar convection model problem, and results are obtained which suggest that the algorithm is both conditionally stable and rapidly convergent when nonperiodic inflowoutflow boundary conditions are used. A new form of artificial dissipation which acts along physical streamlines instead of coordinate grid lines is also tested and found to introduce less error when the local flow direction is not aligned with the computational grid. An accurate solution for a laminar horseshoe vortex flow is computed using an improved solution algorithm with small artificial dissipation. This solution does not change significantly when the mesh spacing is halved using 15 x 15 x 15 and 29 x 29 x 29 grids. Very good convergence rates were obtained, such that residuals were reduced by a factor of 1100 in 30 and 60 iterations respectively, for 3,375 and 24,389 grid points. Author.

# Descriptors:

# Subject Categories:

- Theoretical Mathematics
- Fluid Mechanics