Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Chorin, A. J., “A Numerical Method for Solving Incompressible Viscous Flow Problems,” Journal of Computational Physics, Vol. 2, 1967, pp. 12–26.
Chakravarthy, S. R. and Osher, S.,“A New Class of High Accuracy TVD Schemes for Hyperbolic Conservation Laws,” AIAA Paper No. 85-0363, 1985.
Chakravarthy, S. R. and Ota, D. K., “Numerical Issues in Computing Inviscid Supersonic Flow Over Conical Delta Wings,” AIAA Paper No. 86-0440, 1986.
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.
Pulliam, T. H. and Steger, J. L., “Recent Improvements in Efficiency, Accuracy, and Convergence for Implicit Factorization Algorithms,” AIAA Paper No. 85-0360, 1985.
Jameson, A. and Yoon, S., “Multigrid Solution of the Euler Equations Using Implicit Schemes,” AIAA Journal, Vol 24, November 1986, pp. 1737–1743.
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.
Gorski, J. J., “High Accuracy TVD Schemes for the k-e Equations of Turbulence,” AIAA Paper No. 85-1665, 1985.
Gorski, J. J., “A New Near-Wall Formulation for the k-e Equations of Turbulence,” AIAA Paper No. 86-0556, 1986.
Escudier, M. P., “Observations of the Flow Produced in a Cylindrical Container by a Rotating Endwall,” Experimental Fluids, Vol 2, 1984, p. 189.
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.
Baker, C. J., “The Laminar Horseshoe Vortex,” Journal of Fluid Mechanics, Vol. 95, part 2, 1979, pp. 347–367.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Springer-Verlag
About this paper
Cite this paper
Gorski, J.J. (1989). Solutions of the incompressible Navier-Stokes equations using an upwind -differenced TVD scheme. In: Dwoyer, D.L., Hussaini, M.Y., Voigt, R.G. (eds) 11th International Conference on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics, vol 323. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51048-6_41
Download citation
DOI: https://doi.org/10.1007/3-540-51048-6_41
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51048-2
Online ISBN: 978-3-540-46141-8
eBook Packages: Springer Book Archive