Abstract
The vorticity formulation of the Navier-Stokes equations is described in connection to a free-Lagrangian approach for the treatment of vorticity diffusion. The position of the vortices is updated according to the fluid velocity, suitably reconstructed from the vortex distribution. The strengths satisfy a diffusion equation discretized on the irregular grid of the vortices. Its implementation is based on the discretization of the Laplacian on the particle grid and is obtained with the use of a Voronoi diagram that is updated in O(N) operations at each time step. The scheme for the diffusion term is conservative and there is an energy estimate (total “energy” associated with vortices decreases). The comparison to the exact solution shows a second order spatial convergence. The problem of an elastic flag in a fluid is under investigation. Preliminary results are shown.
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© 1991 Springer-Verlag
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Russo, G. (1991). Deterministic vortex methods for the incompressible Navier-Stokes equations. In: Trease, H.E., Fritts, M.F., Crowley, W.P. (eds) Advances in the Free-Lagrange Method Including Contributions on Adaptive Gridding and the Smooth Particle Hydrodynamics Method. Lecture Notes in Physics, vol 395. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54960-9_63
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DOI: https://doi.org/10.1007/3-540-54960-9_63
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