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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Viscous flow in domains with corners: Numerical artifacts, their origin and removal
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Viscous flow in domains with corners: Numerical artifacts, their origin and removal

机译：带有拐角的区域中的粘滞流动：数值假象，它们的起源和去除

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摘要

Viscous flows in domains with boundaries forming two-dimensional comers are considered. We examine Che case where on each side of the corner the boundary condition for the tangential velocity is formulated in terms of stress. It is shown that computing such flows numerically by straightforwardly applying well-tested algorithms (and numerical codes based on their use, such as COMSOL Multiphysics) can lead to spurious multivaluedness and mesh-dependence in the distribution of the fluid's pressure. The origin of this difficulty is that, near a corner formed by smooth parts of the boundary, in addition to the solution of the formulated inhomogeneous problem, there also exists an eigensolution. For obtuse corner angles this eigensolution (a) becomes dominant and (b) has a singular radial derivative of velocity at the corner. Despite the bulk pressure in the eigensolution being constant, when the derivatives of the velocity are singular, numerical errors in the velocities calculation near the corner give rise to pressure spikes, whose magnitude increases as the mesh is refined. A method is developed that uses the knowledge about the eigensolution to remove the artifacts in the pressure distribution. The method is first explained in the simple case of a Stokes flow in a corner region and then generalized for the Navier-Stokes equations applied to describe steady and unsteady free-surface flows encountered in problems of dynamic wetting.
机译：考虑在边界形成二维角的区域中的粘性流动。我们研究了切角情况下切线速度的边界条件是根据应力来表示的情况。结果表明，通过直接应用经过良好测试的算法（以及基于其使用的数字代码，例如COMSOL Multiphysics）直接计算数值，会导致流体压力分布中的虚假多值和网格相关性。该困难的根源在于，在边界的光滑部分形成的拐角附近，除了所提出的不均匀问题的解决方案之外，还存在本征解决方案。对于钝角角，本征解（a）占主导，（b）在角处具有速度的奇异径向导数。尽管本征解中的整体压力是恒定的，但当速度的导数为奇数时，拐角附近速度计算中的数值误差会导致压力峰值，压力峰值随着网格的细化而增加。开发了一种方法，该方法使用了有关本征解的知识来消除压力分布中的伪影。首先在拐角区域的斯托克斯流的简单情况下解释该方法，然后将其推广到用于描述动态润湿问题中遇到的稳态和​​非稳态自由表面流的Navier-Stokes方程。

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