Solutions of the incompressible Navier-Stokes equations using an upwind -differenced TVD scheme
The Navier-Stokes equations for incompressible fluid flows have been solved using the pseudo-compressibility concept. The equations are discretized using a third order accurate upwind differenced Total Variational Diminishing (TVD) scheme for the convection terms. The equations are solved implicitly and complex geometries are split into multiple blocks for which structured grids can be generated. This method of solving the Navier-Stokes equations has been implemented in the David Taylor Navier-Stokes (DTNS) series of computer codes. Solutions are provided for several cases including the two-dimensional flow over an airfoil, the axisymmetric flow in a cylindrical container with a rotating lid, and the three-dimensional flow around a circular cylinder mounted on a flat-plate. These results demonstrate the wide applicability of the DTNS computer codes.
KeywordsCircular Cylinder AIAA Paper Horseshoe Vortex Vortex Breakdown Cylindrical Container
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- Chorin, A. J., “A Numerical Method for Solving Incompressible Viscous Flow Problems,” Journal of Computational Physics, Vol. 2, 1967, pp. 12–26.Google Scholar
- Chakravarthy, S. R. and Osher, S.,“A New Class of High Accuracy TVD Schemes for Hyperbolic Conservation Laws,” AIAA Paper No. 85-0363, 1985.Google Scholar
- Chakravarthy, S. R. and Ota, D. K., “Numerical Issues in Computing Inviscid Supersonic Flow Over Conical Delta Wings,” AIAA Paper No. 86-0440, 1986.Google Scholar
- Gorski, J. J., “TVD Solutions of the Incompressible Navier-Stokes Equations With an Implicit Multigrid Scheme,” to be presented at the First National Fluid Dynamics Conference, Cincinnati, Ohio, July 24–28, 1988.Google Scholar
- Pulliam, T. H. and Steger, J. L., “Recent Improvements in Efficiency, Accuracy, and Convergence for Implicit Factorization Algorithms,” AIAA Paper No. 85-0360, 1985.Google Scholar
- Jameson, A. and Yoon, S., “Multigrid Solution of the Euler Equations Using Implicit Schemes,” AIAA Journal, Vol 24, November 1986, pp. 1737–1743.Google Scholar
- Coles, D. and Wadcock, A. J. “Flying Hot Wire Study of Flow Past an NACA 4412 Airfoil at Maximum Lift,” AIAA Journal, April, 1979, pp. 321–329.Google Scholar
- Gorski, J. J., “High Accuracy TVD Schemes for the k-e Equations of Turbulence,” AIAA Paper No. 85-1665, 1985.Google Scholar
- Gorski, J. J., “A New Near-Wall Formulation for the k-e Equations of Turbulence,” AIAA Paper No. 86-0556, 1986.Google Scholar
- Escudier, M. P., “Observations of the Flow Produced in a Cylindrical Container by a Rotating Endwall,” Experimental Fluids, Vol 2, 1984, p. 189.Google Scholar
- Lugt, H. J. and Abboud, M., “Axisymmetric Vortex Breakdown With and Without Temperature Effects in a Container With a Rotating Lid,” Journal of Fluid Mechanics, Vol. 179, 1987; pp. 179–200.Google Scholar
- Baker, C. J., “The Laminar Horseshoe Vortex,” Journal of Fluid Mechanics, Vol. 95, part 2, 1979, pp. 347–367.Google Scholar