Variationally Optimized Vortex Tracing Algorithm for Three-Dimensional Flows around Solid Bodies

摘要

The construction of vortex models for two and three-dimensional viscous flows around solid bodies is addressed. A Lagrangian formulation of the inviscid vorticity transport equation is treated using a flow map. This formulation can be converted into a Hamiltonian description which is used in the definition and proof of convergence of a stochastic algorithm for the solution of the viscous vorticity transport equation. Numerical algorithms for the solution of two-dimensional flow fields and for the solution of the three-dimensional flow field around a circular cylinder using the Lagrangian functional are presented. Forces on a body in a viscous fluid are determined. The initial stage of the wake of an impulsively started cylinder; the vortex formation around cylinders in steady flow or oscillating harmonically; and the forces on cylinders in these flows are calculated. Test results of the numerical algorithm for the determination of the vector stream function for the three-dimensional flow field around a circular cylinder are discussed.