Unsteady analysis of bluff bodies using the nonlinear disturbance equations

The study of inviscid and viscous unsteady fluid flow is made using the finite volume method solving the nonlinear disturbance equations. Both structured, two-dimensional and unstructured, three-dimensional cases are tested to determine the advantages of using the nonlinear disturbance equation formulation for unsteady analysis with explicit time marching. The three-dimensional tests include turbulence modeling using a fixed coefficient Smagorinsky subgrid scale model. A description of the three-dimensional code is provided along with details of modifications made to support parallel operation using the Message Passing Interface library of subroutines. An evaluation of parallel performance is made for the three-dimensional code on different distributed memory, parallel computer systems.; The two-dimensional numerical method consists of a second order, cell-centered scheme using central approximations for flux calculations. Explicit artificial dissipation is used for numerical stability. The comparison using a standard Navier-Stokes formulation is made with the nonlinear disturbance equation formulation for a circular cylinder at Reynolds number 1000, based on freestream velocity and cylinder diameter. The effect of three different types of mean flow inputs to the nonlinear disturbance equation algorithm on the accuracy of the cylinder flow is evaluated. It is found that using the freestream conditions as the mean flow improves the accuracy of the predicted shedding frequency and requires fewer iterations before unsteadiness and periodicity begin.; The three-dimensional numerical method is a second order, unstructured, cell-centered scheme using Roe's approximate Riemann solver to calculate the fluxes. The comparison is made between the standard Navier-Stokes formulation, the standard formulation with the Smagorinsky subgrid scale model, and the nonlinear disturbance equation formulation with the Smagorinsky subgrid scale model. Key parameters, including Reynolds stresses, are compared for the different cases with experiment for the time-averaged flow over a circular cylinder at Reynolds number 3900. All cases were strongly affected by the numerical dissipation inherent in upwind biasing, causing excessive drag and shortened recirculation zones. The nonlinear disturbance equation formulation demonstrated no significant advantages when employed in the three-dimensional case.