Abstract
A new approach is developed for the no-slip boundary condition in vortex methods. The procedure of double layer potential density reconstruction is considered, which consist of two steps. Firstly the integral equation with respect to vortex sheet intensity is solved, which expresses the equality between the tangential components of flow velocity limit value and the body surface velocity. It is solved by using a Galerkin approach. Secondly, the least-squares procedure is implemented, which permits to find nodal values of the potential. It is shown that the developed algorithm makes it possible to improve significantly the quality of solution for the bodies with very complicated geometry and low-quality surface meshes. It can be useful for CFD applications and visual effects reproducing in computer graphics.
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Cottet, G.-H., Koumoutsakos, P.: Vortex Methods: Theory and Practice. Cambridge University Press, Cambridge (2000)
Kempka, S.N., et al.: Accuracy considerations for implementing velocity boundary conditions in vorticity formulations. SANDIA Report SAND96-0583 UC-700 (1996). https://doi.org/10.2172/242701
Lewis, R.I.: Vortex Element Methods for Fluid Dynamic Analysis of Engineering Systems. Cambridge University Press, Cambridge (2005)
Lifanov, I.K., Poltavskii, L.N., Vainikko, G.M.: Hypersingular Integral Equations and Their Applications. CRC Press, Boca Raton (2003)
Marchevsky, I.K., Shcheglov, G.A.: Efficient Semi-Analytical Integration of Vortex Sheet Influence in 3D Vortex Method. In: Wriggers P., et al. (eds.) 5th International Conference on Particle-Based Methods—Fundamentals and Applications, PARTICLES 2017, Hannower (2017)
Marchevsky, I.K., Shcheglov, G.A.: Semi-analytical influence computation for vortex sheet with piecewise constant intensity distribution in 3D vortex methods. In: Proceedings of the 6th European Conference on Computational Mechanics (ECCM 6), 7th European Conference on Computational Fluid Dynamics (ECFD 7), Glasgow (2018)
Saffman, P.G.: Vortex Dynamics. Cambridge University Press, Cambridge (1992)
Shcheglov, G.A., Dergachev, S.A.: Hydrodynamic loads simulation for 3D bluff bodies by using the vortex loops based modification of the vortex particle method. In: Wriggers P., et al. (eds.) 5th International Conference on Particle-Based Methods—Fundamentals and Applications, PARTICLES 2017, Hannower (2017)
Weissmann, S., Pinkall, U.: Filament-based smoke with vortex shedding and variational reconnection. In: 37th International Conference and Exhibit on Computer Graphics and Interactive Technologies, Los Angeles (2010)
Acknowledgement
The research is supported by Russian Science Foundation (proj. 17-79-20445).
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Marchevsky, I.K., Shcheglov, G.A. (2020). Double Layer Potential Density Reconstruction Procedure for 3D Vortex Methods. In: van Brummelen, H., Corsini, A., Perotto, S., Rozza, G. (eds) Numerical Methods for Flows. Lecture Notes in Computational Science and Engineering, vol 132. Springer, Cham. https://doi.org/10.1007/978-3-030-30705-9_25
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DOI: https://doi.org/10.1007/978-3-030-30705-9_25
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