Parameter Sensitivity of an Eddy Viscosity Model: Analysis, Computation and Its Application to Quantifying Model Reliability

An eddy viscosity model can be used as a computationally tractable alternative to that of the Navier-Stokes equations. Model errors immediately become a concern when considering such an approach, and quantifying this error is essential to understanding and using model predictions within an engineering design process. In this paper, sensitivity analysis is presented for a subgrid eddy viscosity model with respect to variations of the eddy viscosity parameter. We demonstrate the analysis utilizing the sensitivity equation method. Approximating the sensitivity requires the solution of the eddy viscosity model. Therefore, the eddy viscosity model and sensitivity equation are coupled in our analysis and computations. An implicit-explicit time-stepping method is developed and analyzed for this set of equations. Our numerical assessments present the role of the sensitivity in quantifying the modeling error arising from the choice of various values of the eddy viscosity parameter. The sensitivity computation allows one to identify an interval of reliability for the eddy viscosity parameter. This gives the user a range of parameter values for which the eddy viscosity model can be considered to be a reliable approximation to the Navier-Stokes equations. A two-dimensional cavity problem is used to illustrate the ideas. In addition, for the standard model problem of two-dimensional flow around a cylinder, the sensitivity computations are shown to be very useful in improving the flow functional approximations that may be used within an optimal design algorithm.