Vorticity Transport on a Lagrangian Tetrahedral Mesh

A Triangulated Vortex Method for the Axisymmetric Euler Equations

“…A problem in testing the method is that the axisymmetric problem does not have the wide range of analytical solutions available for the two-dimensional problem. An obvious reference would be Hill's spherical vortex, which has been used as a test case for other axisymmetric vortex problems [14,15], as have the related Norbury rings [17]. These are unsuitable as general test cases for the method of this paper, however, because they are based on a vorticity distribution ∝ r , precisely that which is used in the development of the present technique.…”

“…Vorticity distribution in r − z plane. described above, or, as in this paper, a triangulation method [6,7,15,23]. The problem then is how to evaluate the integrals.…”

“…Vorticity is assumed to vary in a piecewise linear manner over each triangle and the boundary of the vorticity is clearly defined. This approach was initially developed for twodimensional flows [23] and later extended to two-dimensional flows around solid bodies [6,7] and to three-dimensional flows [15]. In this paper, the method will be extended to axisymmetric flows, using a novel method for the evaluation of the Biot-Savart integral, which does not directly compute element-element interactions and so reduces the computational cost of the velocity calculations.…”

A Lagrangian vortex method for unbounded flows

“…This is a technique used by a number of researchers to compute planar, axisymmetric and three-dimensional flows [11][12][13][14]17]. In it, a Delauanay triangulation connects the vorticity nodes and the triangulation can then be used in extracting the required information from the vorticity distribution.…”

A hybrid vortex method for the simulation of three‐dimensional flows

“…Lagrangian vorticity methods, on the other hand, follow an alternative approach, in which the vorticity-velocity form of Navier-Stokes equations only needed to be solved within the limited 32 W. LI AND M. VEZZA vorticity-containing regions, so that they appear to be efficient and self-adaptive [1][2][3][4]. Since the nonlinear convection term is included in the vorticity time derivative, Lagrangian vorticity methods exhibit little or no numerical dissipation.…”