科研之友
微信
新浪微博
Facebook
分享链接
摘要
We report a slowly-developing, spurious numerical solution in pseudo-spectral direct numerical simulation (DNS) of incompressible fluid turbulence. When the effect of machine round-off on the divergence-free condition is not carefully controlled, a problem can develop slowly (over about 50 large-eddy turnover times) and eventually leads to an unphysical flow field. The problem was found with a previously published, highly-compact algorithm for pseudo-spectral DNS and therefore it is important to document the contamination of this numerical artifact on simulated turbulence structure and statistics. This is a striking example since the problem is not easily noticeable due to its very long development time, and it does not lead to numerical instability but rather a different flow state. A theory is developed to explain the unphysical evolution and predicts the exponential growth of round-off error induced velocity divergence. The theory shows that any correlation of the large-scale forcing with the velocity field at the beginning of the time step could lead to amplification of the velocity divergence. For this reason, the problem is quite reproducible. Several simple remedies are tested and shown to correct the problem. It is shown that all revised algorithms are identical theoretically to the original algorithm, with the only difference in the level of control for the divergence-free condition of the simulated flow field. A general recommendation is that the pressure projection operation should be performed at the end of each time step to ensure that the divergence-free condition is not contaminated by machine round-off.
- 出版日期2009-12
