Vorticity transport on a Lagrangian tetrahedral mesh

An integral vorticity method for computation of incompressible, three-dimen sional, viscous fluid flows is introduced which is based on a tetrahedral m esh that is fit to Lagrangian computational points. A fast method for appro ximation of Biot-Savart type integrals over the tetrahedral elements is int roduced, which uses an analytical expression for the nearest few elements, Gaussian quadratures for moderately distant elements, and a multipole expan sion acceleration procedure for distant elements. Differentiation is perfor med using a moving least-squares procedure, which maintains between first- and second-order accuracy for irregularly spaced points. The moving least-s quares method is used to approximate the stretching and diffusion terms in the vorticity transport equation at each Lagrangian computational point. A new algorithm for the vorticity boundary condition on the surface of an imm ersed rigid body is developed that accounts for the effect of boundary vort icity values both on the total vorticity contained within tetrahedra attach ed to boundary points and on vorticity diffusion from the surface during th e time step. Sample computations are presented for uniform flow past a sphe re at Reynolds number 100, as well as computations for validation of specif ic algorithms. (C) 2000 Academic Press.