求解非定常不可压湍流的SMAC隐式方法

基于简化标记和单元(Simplified marker and cell，SMAC)方法，发展一种在任意曲线坐标系中求解三维非定常不可压湍流Reynolds时均方程的隐式数值方法。控制方程包括以逆变速度为变量的动量方程、压力Poisson方程和k–e 湍流模型方程，控制方程的离散在三维标记和单元(Marker and cell，MAC)交错网格系统中进行。为提高方程数值计算的稳定性，动量方程、k方程和e 方程对流项离散均采用Chakravarthy-Osher总变差衰减(Total variation diminishing，TVD)格式。动量方程、k方程和e 方程离散后的代数方程组采用循环三对角阵算法(Cyclic tridiagonal matrix algorithm，CTDMA)方法进行求解，Poisson方程离散后的代数方程组采用Tschebyscheff超线性松弛(Successive linear over relaxation，SLOR)方法交替方向迭代求解。用该方法自编程序对简化后的射流放水阀内非定常流场进行数值模拟，计算结果和试验结果吻合。

IMPLICIT SMAC METHOD FOR UNSTEADY INCOMPRESSIBLE TURBULENT FLOW

An implicit numerical method is developed based on the simplified marker and cell (SMAC) method to solve the 3D unsteady incompressible turbulence Reynolds-averaging equa-tions in general curvilinear coordinates. The governing equa-tions include the Reynolds averaged momentum equations with contravariant velocities as the unknown variables, pressure Poisson equation and k–e turbulent model equations. The gov-erning equations are discretized in 3D MAC staggered grid. To improve the numerical stability of the implicit SMAC scheme, the higher-order high resolution Chakravarthy-Osher total variation diminishing(TVD) scheme is used to discretize the convective terms in momentum equations and k–e equations. The algebraic equations of momentum equations and k–e equa-tions are solved by cyclic tridiagonal matrix algorithm (CTDMA) method. The algebraic Poisson equations are solved by the Tschebyscheff successive linear over relaxation(SLOR) method with alternating computational directions. The unsteady flows in a simplified hollow-jet valve are simulated with the code written by the first author. The computational results are in satisfactory agreement with the experimental photographs.