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A Further Improvement on the Resurrected Core-Spreading Vortex Method

Authors: M-J. Huang, C-J. Huang, L-C. Chen

Abstract:

In a previously developed fast vortex method, the diffusion of the vortex sheet induced at the solid wall by the no-slip boundary conditions was modeled according to the approximation solution of Koumoutsakos and converted into discrete blobs in the vicinity of the wall. This scheme had been successfully applied to a simulation of the flow induced with an impulsively initiated circular cylinder. In this work, further modifications on this vortex method are attempted, including replacing the approximation solution by the boundary-element-method solution, incorporating a new algorithm for handling the over-weak vortex blobs, and diffusing the vortex sheet circulation in a new way suitable for high-curvature solid bodies. The accuracy is thus largely improved. The predictions of lift and drag coefficients for a uniform flow past a NASA airfoil agree well with the existing literature.

Keywords: Resurrected core-spreading vortex method, Boundaryelement method, Vortex sheet, Over-weak vortex blobs.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1056645

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[1] M.J. Huang, H.X. Su, and L.C. Chen "A fast resurrected core-spreading vortex method with no-slip boundary conditions," J. Comput. Phys. 228, pp.1916-1931, 2009.
[2] A. Leonard, "Vortex methods for flow simulation," J. Comput. Phys. 37, pp.289-335, 1980.
[3] L. Rossi, "Resurrecting core spreading vortex methods: A new scheme that is both deterministic and convergent," SIAM J.Sci.Comp. 17, pp.370-397, 1996.
[4] M.J. Huang, "Diffusion via splitting and remeshing via merging in vortex method," Int. J. Numer. Meth. Fluids 48, pp.521-539, 2005.
[5] C. Chang and R. Chern, "A numerical study of flow around an impulsively started circular cylinder by a deterministic vortex method," J. Fluid Mech 223, pp.243-263, 1991.
[6] Z.Y. Lu and S.F. Shen, "Numerical Methods in Laminar and Turbulent Flow," Pineridge Press, Swansea, UK 5, p.619, 1987.
[7] Z.Y. Lu and T.J. Ross, "Diffusing-vortex numerical scheme for solving incompressible Navier-Stokes equations," J. Comput. Phys. 95, 1991, pp.400-435.
[8] P. Degond and S. Mas-Gallic, "The weighted particle method for convection-diffusion equations. Part 1: The case of an isotropic viscosity," Math. Comput. 53, pp. 485-507, 1989.
[9] D. Fishelov, "A new vortex scheme for viscous flow," J. Comput. Phys. 86, pp. 211-224, 1990.
[10] S. Shankar and L.L. van Dommelen, "A new diffusion procedure for vortex methods," J. Comput. Phys. 127, pp.88-109, 1996.
[11] L.L. Van Dommelen and S. Shankar, "Two counter-rotating diffusing vortices," Phys. Fluids A 7, pp. 808-819, 1995.
[12] Prem K. Kythe, "An introduction to boundary element methods," CRC Press, Boca Raton, 1995.
[13] P. Koumoutsakos, A. Leonard, and F. Pepin, "Boundary condition for viscous vortex methods," J. Comput. Phys. 113, pp.52-61, 1994.
[14] C. Greengard, "The core-spreading vortex method approximations the wrong equation," J. Comput. Phys. 61, pp.345 -348, 1985.
[15] J. Carrier, L. Greengard, and V. Rokhlin, "A fast adaptive multipole algorithm for particle simulations," SIAM J. Sci. Stat.Comput. 9, pp.669-686, 1988.
[16] N.R. Clarke, and O.R. Tutty, "Construction and validation of a discrete vortex method for the two-dimensional incompressible Navier-Stokes equations," Comput. Fluids 23, pp.751-783, 1994.
[17] P. Ploumhans and G.S. Winckelmans, "Vortex methods for high-resolution simulations of viscous flow past bluff bodies of general geometry," J. Comput. Phys. 165, pp.364-406, 2000.