混合解析/数值方法及其在湍流数值模拟上的应用

针对带小时间尺度的源项的方程描述的流动问题,提出了混合解析/数值方法。混合解析/数值方法的基本思想是:分裂原始方程组为对流-扩散部分的偏微分方程和源项的常微分方程。偏微分方程采用合适的数值方法求解,而常微分方程采用解析方式积分。模型方程的理论误差研究表明,混合方法提高了源项处理的精度,降低了混合方法的整体数值误差。分析同时表明,基于时间分裂的算法在求解含源项双曲系统的定常类型问题,会存在数值振荡。为此发展了非分裂方式的混合解析/数值方法,在湍流模型数值计算中提高了数值稳定性,而且加快了计算的收敛速度。

Mixed Analytical/Numerical Method and Its Application to Problems of Turbulent Flow Simulation

The basic concept of mixed method is to split the original set of equations into a Part Differential Equation (PDE) for the convection-diffusion part, and an Ordinary Differential Equation (ODE) for the source term. The PDE is solved by a conventional numerical method, while the ODE is integrated analytically. It is shown that the mixed method improves the accuracy of source term numerical treatment, and is much more accurate than the traditional method. For the two equations turbulence model, the mixed method without time splitting is developed, which allows for convergence to steady state. The application of mixed method on turbulent flow simulation is studied. Numerical result shows that the mixed analytical/numerical method is much better that the conventional method. The mixed method improves the numerical stability, and accelerates the convergence.