Combiningthe Navier‐Stokes systems with Neumann (or natural) boundary condition to characterize a fluid flow is frequent. The popular projection (or pressure correction) methods inspired by Chorin and Temam are not well adapted to such boundary condition, which translate in loss of accuracy. If some alternative projection methods have been proposed to reduce the accuracy loss due to the Neumann condition in case of Newtonian fluids, little has been proposed for generalized Newtonian fluids. In this work, we propose two methods derived from the incremental pressure correction projection that can be used for fluids with inhomogeneous or variable viscosity with natural boundary condition. Both time and space accuracy of the methods will be illustrated using a manufactured solution.

中文翻译：

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具有可变粘度和自然边界条件的Navier-Stokes的投影方案

经常将Navier-Stokes系统与Neumann（或自然）边界条件相结合来表征流体流动。受Chorin和Temam启发的流行的投影（或压力校正）方法不能很好地适应这种边界条件，从而导致精度损失。如果已经提出了一些替代的投影方法来减少由于牛顿流体导致的诺伊曼条件导致的精度损失，那么对于广义牛顿流体的提议就很少了。在这项工作中，我们提出了两种从增量压力校正投影推导的方法，这些方法可用于在自然边界条件下粘度不均匀或可变的流体。将使用制造的解决方案说明方法的时间和空间精度。