Assessment of alternative scale-providing variables in a Reynolds-stress model using high-order methods利用高阶方法在雷诺应力模型中评估替代尺度提供变量

This paper is set in the high-order finite-difference discretization of the Reynolds-averaged Navier-Stokes (RANS) equations, which are coupled with the turbulence model equations. Three alternative scale-providing variables for the specific dissipation rate (ω) are implemented in the framework of the Reynolds stress model (RSM) for improving its robustness. Specifically, g(=1/ω)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g\left( { = 1/\sqrt \omega } \right)$$\end{document} has natural boundary conditions and reduced spatial gradients, and a new numerical constraint is imposed on it; ω˜(=lnω)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde \omega \left( { = \ln \omega } \right)$$\end{document} can preserve positivity and also has reduced spatial gradients; the eddy viscosity νt also has natural boundary conditions and its equation is improved in this work. The solution polynomials of the mean-flow and turbulence-model equations are both reconstructed by the weighted compact nonlinear scheme (WCNS). Moreover, several numerical techniques are introduced to improve the numerical stability of the equation system. A range of canonical as well as industrial turbulent flows are simulated to assess the accuracy and robustness of the scale-transformed models. Numerical results show that the scale-transformed models have significantly improved robustness compared to the ω model and still keep the characteristics of RSM. Therefore, the high-order discretization of the RANS and RSM equations, which number 12 in total, can be successfully achieved.