Unsteady, Laminar Flow Simulations Using the Nonlinear Disturbance Equations

The results of numerical simulations using the Nonlinear Disturbance Equations (NLDE) for viscous test cases in laminar flow are presented. The NLDE are implemented in a two-dimensional, finite volume code to test the algorithm's properties for viscous, wall-bounded flows. Testing focused on the accuracy of unsteady phenomena. An overview of the method, details on the implementation of boundary conditions, and results for a benchmark scattering problem and viscous flow over a circular cylinder are presented. The results show this method converges to a time accurate periodic condition using a variety of inputs for the mean flow field, and under some circumstances may converge substantially faster to the periodic state compared to the same code using a standard Navier-Stokes formulation.