An efficient solver for the RANS equations and a one-equation turbulence model
An efficient solver for the RANS equations and a one-equation turbulence model
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RANS 方程和单方程湍流模型的高效求解器
DOI：
10.1016/j.compfluid.2010.10.010
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发表时间：
2011
影响因子：
2.8
通讯作者：
C. Rossow
中科院分区：
文献类型：
--
作者：
R. Swanson;C. Rossow
具有多重网格和隐式预条件的三步Runge-Kutta(RK)格式是求解流体动力学方程的一种有效方法。采用Baldwin和Lomax的代数湍流模型，对跨声速和低速流动的可压缩雷诺平均N-S方程进行了数值求解。本文研究了当湍流效应用Spalart和Allmaras的单方程模型表示时，RK/隐式格式的收敛问题。该格式对RANS方程和湍流模型的偏微分方程组进行了松散耦合求解。该方法允许检查每个系统的收敛行为。用点对称Gauss-Seidel和局部线松弛相结合的方法来逼近RANS解算器隐式算子的逆。对于湍流方程的求解，我们考虑了三种可供选择的方法：对角占优交替方向隐式格式(DDADI)、对称线高斯-塞德尔格式(SLGS)和隐式预条件两阶段RK格式。给出了翼型流动的计算结果，并与实验数据进行了比较。我们证明了采用RK/隐式格式的间接耦合算法可以有效地求解用于湍流模拟的二维RANS方程和传输型方程。
A three-stage Runge-Kutta (RK) scheme with multigrid and an implicit preconditioner has been shown to be an effective solver for the fluid dynamic equations. Using the algebraic turbulence model of Baldwin and Lomax, this scheme has been used to solve the compressible Reynolds-averaged Navier–Stokes (RANS) equations for transonic and low-speed flows. In this paper we focus on the convergence of the RK/Implicit scheme when the effects of turbulence are represented by the one-equation model of Spalart and Allmaras. With the present scheme the RANS equations and the partial differential equation of the turbulence model are solved in a loosely coupled manner. This approach allows the convergence behavior of each system to be examined. Point symmetric Gauss-Seidel supplemented with local line relaxation is used to approximate the inverse of the implicit operator of the RANS solver. To solve the turbulence equation we consider three alternative methods: diagonally dominant alternating direction implicit (DDADI), symmetric line Gauss-Seidel (SLGS), and a two-stage RK scheme with implicit preconditioning. Computational results are presented for airfoil flows, and comparisons are made with experimental data. We demonstrate that the two-dimensional RANS equations and a transport-type equation for turbulence modeling can be efficiently solved with an indirectly coupled algorithm that uses RK/Implicit schemes.