Abstract
We introduce a pure-streamfunction formulation for the incompressible Navier-Stokes equations. The idea is to replace the vorticity in the vorticity- streamfunction evolution equation by the Laplacianof the streamfunction. The resulting formulation includes the streamfunction only, thus no inter-function relations need to invoked. A compact numerical scheme, which interpolates streamfunction values as well as its first order derivatives, is presented and analyzed.
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References
I. Altas, J. Dym, M. M. Gupta, and R. P Manohar. Mutigrid solution of automatically generated high-order discretizations for the biharmonic equation. SIAM J.Sci.Comput., 19:1575–1585, 1998.
M. Ben-Artzi, D. Fishelov, and S. Trachtenberg. Vorticity dynamics and numerical resolution of navier-stokes equations. Math. Model. Numer. Anal., 35(2):313–330, 2001.
A. J. Chorin and J. E. Marsden. A Mathematical Introduction to Fluid Mechanics. Springer-Verlag, 2-nd edition, 1990.
U. Ghia, K. N. Ghia, and C. T. Shin. High-re solutions for incompressible flow using the navier-stokes equations and a multigrid method. J. Comp. Phys., 48:387–411, 1982.
R. Kupferman. A central-difference scheme for a pure streamfunction formulation of incompressible viscous flow. SIAM J. Sci.Comput., 23, No. 1:1–18, 2001.
T. W. Pan and R. Glowinski. A projection/wave-like equation method for the numerical simulation of incompressible viscous fluid flow modeled by the navierstokes equations. Comput. Fluid Dynamics, 9, 2000.
J. W. Stephenson. Single cell discretizations of order two and four for biharmonic problems. J.Comp.Phys., 55:65–80, 1984.
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Fishelov, D., Ben-Artzi, M., Croisille, JP. (2003). A Compact Scheme for the Streamfunction Formulation of Navier-Stokes Equations. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2667. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44839-X_85
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DOI: https://doi.org/10.1007/3-540-44839-X_85
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