Multigrid unsteady navier-stokes calculations with aeroelastic applications

An implicit approach to the solution of the unsteady two-dimensional Navier-Stokes equations is presented. After spatial discretization, the resulting set of coupled implicit non-linear equations is solved iteratively. This is accomplished using well proven convergence acceleration techniquies for explicit schemes such as multigrid, residual averaging, and local time-stepping in order to achieve large computational efficiency in the calculation. Calculations are performed in parallel using a domain decomposition technique with optimized communication requirements. In addition, particular care is taken to minimize the effect of numerical dissipation with flux-limited dissipation schemes. Results for the unsteady shedding flow behind a circular cylinder and for a pitching NACA 64A010 airfoil are presented with experimental comparisons, showing the feasibility of accurate, efficient, time-dependent viscons calculations. Finally, a two-dimensional structural model of the cylinder is coupled with the unsteady flow solution, and time responses of the deflections of the structure are analyzed.