Verified predictions of shape sensitivities in wall-bounded turbulent flows by an adaptive finite-element method

JOURNAL OF COMPUTATIONAL PHYSICS

卷:228

Article

Hay, A.¹  Pelletier, D.¹  Di Caro, R.¹ 

[1] Ecole Polytech, Dept Genie Mecan, Montreal, PQ H3C 3A7, Canada

关键词: Sensitivity Analysis;    Sensitivity Equation Method;    Turbulent flows;    RANS equations;    k-epsilon model;    Wall functions;    Adaptive finite-element method;    Verification and Validation;   

DOI  :  10.1016/j.jcp.2009.03.022

来源: Elsevier

【 摘 要 】

A Continuous Sensitivity Equation (CSE) method is presented for shape parameters in turbulent wall-bounded flows modeled with the standard k-epsilon turbulence model with wall functions. Differentiation of boundary conditions and their complex dependencies on shape parameters, including the two-velocity scale wall functions, is presented in details along with the appropriate methodology required for the CSE method. To ensure accuracy, grid convergence and to reduce computational time, an adaptive finite-element method driven by asymptotically exact error estimations is used. The adaptive process is controlled by error estimates on both flow and sensitivity solutions. Firstly, the proposed approach is applied on a problem with a closed-form solution, derived using the Method of the Manufactured Solution to perform Code Verification. Results from adaptive grid refinement studies show Verification of flow and sensitivity solvers. error estimators and the adaptive strategy. Secondly, we consider turbulent flows around a square cross-section cylinder in proximity of a solid wall. We examine the quality of the numerical solutions by performing Solution Verification and Validation. Then, Sensitivity Analysis of these turbulent flows is performed to investigate the ability of the method to deal with non-trivial geometrical changes. Sensitivity information is used to estimate uncertainties in the flow solution caused by uncertainties in the shape parameter and to perform fast evaluation of flows on nearby configurations. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free