In this short note, we discuss the circumstances that can lead to a failure to observe design order of discretization error convergence in accuracy verification when solving a time-dependent problem. Intuitively, one would expect to observe a design spatial order of accuracy when the discretization error is measured on a series of consistently refined grids after one extremely small time step because the time integration is then nearly exact. However, in reality, one observes one-order lower discretization error convergence than the design order. This loss of accuracy is not necessarily resolved even if the time step is consistently reduced along with the grid refinement. This can cause a serious problem because then one would wind up trying to find a coding error that does not exist. This short note clarifies the mechanism causing this failure to observe a design order of discretization error convergence in accuracy verification when solving time-dependent problems, and provides a guide for avoiding such pitfalls.

翻译：在这篇短文中，我们讨论了在求解时间依赖问题时，可能导致精度验证中无法观察到离散化误差收敛的设计阶数的情形。直观上，当在一系列一致性加密的网格上，经过一个极小时的时间步长后测量离散化误差时，人们会期望观察到设计空间精度阶数，因为此时时间积分近乎精确。然而，实际中观察到的离散化误差收敛阶数比设计阶数低一阶。即使随着网格加密一致地减小时间步长，这种精度损失也未必能得到解决。这可能导致严重问题，因为人们最终会试图查找并不存在的编码错误。本文阐明了在求解时间依赖问题时，导致精度验证中无法观察到离散化误差收敛设计阶数这一现象的机制，并提供了避免此类陷阱的指南。