二维无界自由衰减流的数值研究

Numerical Simulations of 2D Free Decaying Flow in an Unbounded Domain

无界区域上的流体运动是流体力学中的热点和难点问题.采用传统的扩大计算区域算法和新发展的基于无界区域的Hermite基函数算法对二维无界区域的自由衰减流动进行研究.结果发现,对于只存在相同符号涡的初始流场而言,两种方法都可以得出正确的结果;而对于正负涡都存在的初始流场,传统方法即便利用非常大的计算区域也无法进行正确的长时间模拟,但是新方法却能高效求解.对算例的Hermite算法数值模拟验证了理论解Oseen涡的存在.

The fluid motion in an unbounded domain is an appealing and difficult problem in fluid mechanics. The 2D unbounded free decaying flow was studied and simulated with the traditional extended domain Fourier spectral scheme and the newly developed Hermite spectral algorithm,respectively. The results show that,in the case of only same-signed vortices existing in the domain at the beginning of simulations,both methods give correct results; on the other hand,in the case of positive and negative vortices coexisting initially,the new Hermite spectral method still gives satisfactory results for the problem efficiently even after longtime simulation,but the traditional Fourier method hardly yields correct results even in a greatly extended computing domain. Moreover,the numerical simulations of the examples with the Hermite spectral method prove the existence of the theoretically predicted Oseen vortices.