Abstract
A visualization of three-dimensional incompressible flows by divergence-free quasi-two-dimensional projections of the velocity field onto three coordinate planes is revisited. An alternative and more general way to compute the projections is proposed. The approach is based on the Chorin projection combined with a SIMPLE-like iteration. Compared to the previous methodology based on divergence-free Galerkin–Chebyshev bases, this technique, formulated in general curvilinear coordinates, is applicable to any flow region and allows for faster computations. To illustrate this visualization method, examples in Cartesian and spherical coordinates, as well as post-processing of experimental 3D-PTV data, are presented.
Similar content being viewed by others
References
McLaughlin T., Laramee R.S., Peikert R., Post F.H., Chen M.: Over two decades of integration-based, geometric flow visualization. Comput. Gr. Forum 29, 1807–1829 (2010)
Edmunds M., Laramee R.S., Chen G., Max N., Zhang E., Ware C.: Surface-based flow visualization. Comput. Gr. 36, 974–990 (2012)
Etien, T., Nguyen, H., Kirby, R.M., Siva, C.T.: “Flow visualization” juxtaposed with “visualization of flow”: synergistic opportunities between two communities. In: Proceedings of 51st AIAA Aerospace Science Meeting, New Horizon Forum Aerospace Exp., pp. 1–13 (2013)
Schulze M., Martinez Esturo J., Günther T., Rössl C., Seidel H.-P., Weinkauf T., Theisel H.: Sets of Globally Optimal Stream Surfaces for Flow Visualization. Comput. Gr. Forum 33, 1–10 (2014)
Gelfgat A.Yu.: Visualization of three-dimensional incompressible flows by quasi-two-dimensional divergence-free projections. Comput. Fluids 97, 143–155 (2014)
Gelfgat A.Yu.: Oscillatory instability of three-dimensional natural convection of air in a laterally heated cubic box, submitted for publication. (2015). arXiv:1508.00652
Chorin A.J.: Numerical solution of the Navier–Stokes equations. Math. Comput. 22, 745–762 (1968)
Patankar S.V., Spalding D.B.: A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. Int. J. Heat Mass Transf. 15, 1787–1806 (1972)
Patankar S.V.: Numerical Heat Transfer and Fluid Flow. Taylor & Francis, Washington, DC (1980)
Kopachevsky M.D., Krein S.D.: Operator Approach to Linear Problems of Hydrodynamics. Springer, Berlin (2000)
Batchelor G.K.: An Introduction to Fluid Dynamics. Cambridge University Press, Cambridge (2000)
Yoon H.S., Yu D.H., Ha M.Y., Park Y.G.: Three-dimensional natural convection in an enclosure with a sphere at different vertical locations. Int. J. Heat Mass Transf. 53, 3143–3155 (2010)
Gulberg Y., Feldman Y.: On laminar natural convection inside multi-layered spherical shells. Int. J. Heat Mass Transf. 91, 908–921 (2015)
Akutina, Y.: Experimental investigation of flow structures in a shallow embayment using 3D-PTV. PhD thesis, McGill University, Montreal, QC (2015)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Tim Colonius.
Rights and permissions
About this article
Cite this article
Gelfgat, A.Y. Visualization of three-dimensional incompressible flows by quasi-two-dimensional divergence-free projections in arbitrary flow regions. Theor. Comput. Fluid Dyn. 30, 339–348 (2016). https://doi.org/10.1007/s00162-016-0383-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00162-016-0383-z