New Diffusing-Vortex Numerical Scheme for Solving Incompressible Navier-Stokes Equations. Phase 1 Report

摘要

A new numerical algorithm, the diffusing-vortex method for time-dependent two-dimensional Navier-Stokes equations is further developed for extension to general two-dimensional initial value problems and boundary value problems. The hybrid algorithm consists of two-steps in a simulation cycle: a Lagrangian convection simulation for the first time step and a diffusion simulation through the use of new vortex points at fixed Eulerian mesh points for the second time step. The mathematical mechanisms of computation behind the algorithm and its characteristics of convergence and accuracy, are analyzed in applications for the following problems: (1) initial value problem: the decay of a single vortex of finite size and the decay and interaction of a vortex-pair of two finite-core regions; (2) the boundary value problem: the unsteady flow field around a rotating cylinder with high Reynolds number up to 10,000.