Sensitivity computations of eddy viscosity models with an application in drag computation

Abstract

SUMMARYThis paper presents a numerical study of the sensitivity of an eddy viscosity model with respect to the variation of the eddy viscosity parameter for the two-dimensional driven cavity problem and ow around a cylinder. The main objective is to provide a comparison between computing the sensitivity using sensitivity equation and computing the sensitivity using ÿnite di erence methods and also numerically illustrate the application of the sensitivity computations in improving drag ow functional.

Semi‐implicit schemes for transient Navier–Stokes equations and eddy viscosity models

“…Certain LES models use a filtering procedure on Navier-Stokes equations, ultimately solving for the average velocities; e.g., see [1] and [2]. These models can be useful in such applications as the prediction of a hurricane as well as in the estimation of flow functionals involving lift and drag ( [3][4][5][6]). In this study, one such LES model referred to as an Eddy Viscosity model (EVM) is considered.…”

“…Sensitivity computations of (1.1) with respect to the variation of the eddy viscosity parameter α with its applications are carried out in [4]. Research on the use of the methods discussed in this study for sensitivity analysis and computations of (1.1) with respect to α is in progress by the authors.…”

Sensitivity Analysis and Computations of the Time Relaxation Model

“…All calculations presented in this paper were obtained using the publicly available finite element software package FreeFEM++, see [26]. In these studies, we have used the 2D Taylor-Green vortex decay problem and the 2D Cavity problem as our test problems, see [38,39] (for sensitivity computations of two different fluid models with respect to the filter width using 2D Cavity problem). In addition, we examine the sensitivity computations in a three dimensional case study using the 3D Ethier-Steinman benchmark problem, see [16,38] for flow velocity and its sensitivity computations based on the variations of filter width δ.…”

“…To that end, sensitivity analysis techniques provide a measure to compute solution uncertainties due to the variation of the selected parameter and determine a reliable interval for the parameter value. Over the years, there have been studies on the sensitivity of fluid flows in different aspects, [3,9,23,39,41,42]. Assessing model error that leads to uncertainty quantification is an important application of sensitivity analysis, see [35,40] for recent works in this direction.…”

“…While finite difference quotient is easy to compute using a flow solver code, it might not be a reliable technique to compute sensitivites of a fluid model, see [7,22]. In that aspect, the use of CSEM is preffered to that one of the finite difference, see [6,39] for a camparison between these two methods in computing sensitivities. For computing flow sensitivity via CSEM, once the flow solver has converged only a linear solve is needed.…”