低速流预处理Roe格式中的数值粘性

Numerical dissipation of Roe’s scheme with preconditioning for low-speed flows

使用Roe格式计算低马赫数流动,需采用预处理技术.在预处理技术中,需要选择适合的预处理参数,但有时很难找到,因而得不到合理的计算结果.通过数值实验,发现使用预处理方法时,格式的数值粘性对低速流动的模拟有显著的影响.提出了在预处理Roe格式中加入可调参数,用以控制数值粘性对计算结果的影响.带有可调节数值粘性参数的预处理Roe格式的数值粘性更接近低速流动的真实耗散,反映了低速流动的真实物理现象.对方腔流动和圆柱绕流的低雷诺数定常流动所做的数值实验,得到了比较满意的结果,表明这一改进是有效的.对同一低雷诺数不同低马赫数的定常圆柱绕流所做的数值实验,均得到了满意的结果,表明了方法的适用性.

Preconditioning is necessary for simulating of low-speed flows with Roe＇s scheme.With most research on choosing preconditioning parameter,the solution may be wrong.Numerical experiments show the numerical dissipation of the scheme has a notable effect on low-speed flow numerical simulation with preconditioning method.A manner by using an adjustable parameter in preconditioning Roe＇s scheme to control the numerical dissipation was proposed.The numerical dissipation of preconditioning Roe＇s scheme with an adjustable parameter was more similar to the real dissipation of low-speed flows and reflected the real physical phenomena of low-speed flows.Numerical results show the efficiency of the new scheme and the low Reynold-number steady solutions of viscous flow past a circular cylinder and square cavity flow are satisfied.Also indicate that the applicability of the new scheme and different low Mach number with the same low Reynold-number steady solutions of viscous flow past a circular cylinder are also satisfied.