Numerical Errors in Unsteady Flow Simulations
Numerical Errors in Unsteady Flow Simulations
复制标题
非定常流模拟中的数值误差
DOI：
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发表时间：
2019
影响因子：
0.6
通讯作者：
M. Hoekstra
中科院分区：
文献类型：
--
作者：
L. Eça;G. Vaz;S. Toxopeus;M. Hoekstra
本文讨论了非定常流动模拟中的数值误差，包括舍入误差、统计误差、迭代误差和时空离散化误差。讨论了迭代误差和离散化误差的估计以及初始条件对周期非定常流动的影响。在后一种情况下，目标是确定将初始条件的影响降低到可以忽略的程度所需的模拟时间。使用两个一维的非定常人工解来说明不同类型的数值误差之间的干扰。一种解是周期性的，另一种解在达到稳态之前包括一个暂态区域。结果表明，对于选定的网格和时间步长，周期解的统计收敛的误差水平比迭代和离散化误差小得多。然而，当迭代收敛准则的要求降低、网格细化和Courant数增加时，统计收敛性能变差，对于周期流和瞬态流的统计收敛解，与离散化误差相比，获得可忽略的迭代误差影响所需的迭代收敛准则比文献中的典型值更严格。当网格细化和/或库朗特数量增加时，需要更严格的标准。当数值误差被迭代误差所控制时，细化网格和/或减小时间步长是没有意义的。对于数值误差由离散化误差主导的解，采用了三种不同的技术来说明如何使用网格/时间精化研究来估计离散化不确定性：固定Courant数的三个数据点；同一网格的五个数据点和同一时间步的三个网格；包括至少两个网格和两个时间步的五个数据点。后两种技术区分了空间收敛和时间收敛，而前一种技术结合了两种离散化误差的影响。
This article discusses numerical errors in unsteady flow simulations, which may include round-off, statistical, iterative, and time and space discretization errors. The estimation of iterative and discretization errors and the influence of the initial condition on unsteady flows that become periodic are discussed. In this latter case, the goal is to determine the simulation time required to reduce the influence of the initial condition to negligible levels. Two one-dimensional, unsteady manufactured solutions are used to illustrate the interference between the different types of numerical errors. One solution is periodic and the other includes a transient region before it reaches a steady-state. The results show that for a selected grid and time-step, statistical convergence of the periodic solution may be achieved at significant lower error levels than those of iterative and discretization errors. However, statistical convergence deteriorates when iterative convergence criteria become less demanding, grids are refined, and Courant number increased.For statistically converged solutions of the periodic flow and for the transient solution, iterative convergence criteria required to obtain a negligible influence of the iterative error when compared to the discretization error are more strict than typical values found in the open literature. More demanding criteria are required when the grid is refined and/or the Courant number is increased. When the numerical error is dominated by the iterative error, it is pointless to refine the grid and/or reduce the time-step. For solutions with a numerical error dominated by the discretization error, three different techniques are applied to illustrate how the discretization uncertainty can be estimated, using grid/time refinement studies: three data points at a fixed Courant number; five data points involving three time steps for the same grid and three grids for the same time-step; five data points including at least two grids and two time steps. The latter two techniques distinguish between space and time convergence, whereas the first one combines the effect of the two discretization errors.