一种强耦合Spalart-Allmaras湍流模型的RANS方程的高效数值计算方法  

An Efficient Numerical Method for Coupling the RANS Equations with Spalart-Allmaras Turbulence Model Equation

作　　者：杨小权[1,2] 杨爱明[2] 孙刚[2] 

机构地区：[1]上海飞机设计研究院,上海201210 [2]复旦大学力学与工程科学系,上海200433

出　　处：《航空学报》2013年第9期2007-2018,共12页Acta Aeronautica et Astronautica Sinica

基　　金：国家自然科学基金(11172070);复旦大学研究生创新基金(EYH2126022)~~

摘　　要：在工程实际中,一方程湍流模型或两方程湍流模型的求解通常和雷诺平均Navier-Stockes(RANS)方程的求解是解耦的,也称之为松耦合求解。在松耦合求解过程中,RANS方程和湍流模型方程通常采用不同的数值方法异步求解。这种求解方式很容易产生因两者计算精度不一致而引起的额外数值耗散。为了消除这种耗散,将RANS方程与Spalart-Allmaras模型方程耦合成一个系统方程——强耦合RANS方程,并发展了一种用于求解该系统方程的高效强耦合算法,其中对流项离散采用了Roe格式,时间项的离散采用了隐式LU-SGS(Lower-Upper Symmetric Gauss-Seidel)格式,为了提高计算效率,采用了三层V循环多重网格方法。通过翼型/机翼和振荡翼型/机翼等算例验证了本文发展的强耦合算法不仅具有较好的收敛性,而且计算精度明显优于松耦合算法,特别对于阻力的预测,强耦合算法更加准确。In engineering practice, the system of the one- or two-equation turbulence model together with Reynolds-aver- aged Navier-Stokes （RANS） equations is decoupled during its solving, which is known as loosely coupled solving. In the process, RANS equations and turbulence model equations are commonly solved separately with different numerical methods, which may easily incur additional numerical dissipation due to inconsistent calculation accuracy. In order to eliminate this dis- sipation, RANS equations and Spalart-AIImaras model equation are hereby coupled into one strongly coupled system of equa- tions, and an efficient method is developed for its solution. The convective terms are discrete by the Roe scheme, and the time derivative terms are discrete by the LU-SGS （Lower-Upper Symmetric-Gauss-Seidel） method. In order to accelerate the convergence, a three level V-cycle multigrid algorithm is used. Through numerical experiments of the airfoil/wing and os- cillating airfoil/wing, the convergence and accuracy of this algorithm are verified, and results show that its accuracy is signif- icantly better than the loosely coupled algorithm, especially in the prediction of drag force.

关 键 词：Spalart—Allmaras湍流模型 RANS方程 强耦合算法 多重网格方法 双时间方法 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]