Fluid Models and Parameter Sensitivities: Computations and Applications

Abstract

Fluid models were developed as an alternative to the Navier-Stokes equations to avoid computational complexity especially in case of turbulent flows. Model errors due to the sensitivity of a model to user-elected parameters become an immediate concern. Quantifying this error and assessing the reliability of the model given a parameter value are essential to understanding and using model predictions within an engineering design process. This paper presents an overview of sensitivity computations of three fluid models namely the Eddy Viscosity Model, the Leray-Alpha Model, and the Time Relaxation Model to the variations of different model parameters. The 2D Cavity problem is used to numerically illustrate the application of sensitivity computations in identifying the range of parameter values for which the fluid model can be considered a reliable approximation. In addition, testing on the 2D flow around a cylinder, our numerical results support the idea that sensitivity information can incorporate the effects of unresolved scales on flow functionals that leads to an improved estimation. Investigations of flow sensitivity for non-isothermal Stokes flow are presented as well.