A Lagrangian Vortex Method for Simulating Flow Over 3-D Objects

Abstract

A grid-free method for the simulation of incompressible flow over complex 3-D objects is presented. The algorithm is based on the Lagrangian Vortex Element and the Vorticity Redistribution methods to account for vorticity dynamics and diffusion, respectively. The wall velocity boundary conditions are imposed by solving a Petrov-Galerkin discretization of the Fredholm boundary integral equation of the second kind for the vector-valued vortex sheets at the wall. Computations are accelerated using a MPI-parallel adaptive Fast Multipole Method (oct-tree code). In this paper, the computational algorithm is described briefly, and the first in a series of benchmark results presented using the example of flow over a sphere at low Reynolds numbers. Preliminary diagnostics of the present simulations show very good agreement with previously published data.