摘要
We present the approaches to implementing the k-√k L turbulence model within the framework of the high-order discontinuous Galerkin(DG)method.We use the DG discretization to solve the full Reynolds-averaged Navier-Stokes equations.In order to enhance the robustness of approaches,some effective techniques are designed.The HWENO(Hermite weighted essentially non-oscillatory)limiting strategy is adopted for stabilizing the turbulence model variable k.Modifications have been made to the model equation itself by using the auxiliary variable that is always positive.The 2nd-order derivatives of velocities required in computing the von Karman length scale are evaluated in a way to maintain the compactness of DG methods.Numerical results demonstrate that the approaches have achieved the desirable accuracy for both steady and unsteady turbulent simulations.
本文提出了一种在高阶间断Galerkin框架内实现k-√k L湍流模拟的有效方法.本文使用间断Galerkin方法求解离散化的雷诺平均Navier-Stokes方程,通过发展一些有效的技术,提高方法的鲁棒性,包括采用HWENO(Hermite weighted essentially non oscillatory)限制策略来稳定湍流模型变量k,使用保正的辅助变量对模型方程本身进行修改.通过发展计算von Karman长度尺度所需的速度二阶导数的有效方法,保持了DG方法的紧凑性.数值结果表明,本文发展的方法在稳态和非稳态湍流模拟中都达到了较好的预测精度.
基金
supported by the National Natural Science Foundation of China(Grant Nos.92252201 and 11721202)
the Fundamental Research Funds for the Central Universities.
