Vorticity errors in multidimensional Lagrangian codes
Vorticity errors in multidimensional Lagrangian codes
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DOI：
10.1016/0021-9991(92)90280-c
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发表时间：
1992-03
影响因子：
4.1
通讯作者：
J. Dukowicz;B. Meltz
中科院分区：
文献类型：
--
作者：
J. Dukowicz;B. Meltz
以著名的Saltzman检验问题为例，我们研究了在计算一维无旋流时，多维拉格朗日码经历网格缠绕的明显悖论。我们证明了其原因是由非均匀网格产生的虚假涡量或涡度误差。在此基础上，我们研究了两种构造改进的拉格朗日顶点速度的方法，即通过去除或过滤这种虚假涡度，而不是通过更常见的引入人工粘性的做法。第一种方法从已知的流动散度和通过输运方程计算的真实涡量重建速度。第二种方法更简单、更有效，它从速度中减去无散度修正，从而得到的速度具有正确的涡量。然后，我们成功地将该方法应用于二维激波折射问题，该问题表现出非零的内禀涡度。
We investigate the apparent paradox, as exemplified by the well-known Saltzman test problem, of multidimensional lagrangian codes experiencing mesh tangling when computing one-dimensional irrotational flows. We demonstrate that the cause is the generation of spurious vorticity, or vorticity error, by a nonuniform mesh. Based on this, we investigate two methods of constructing improved lagrangian vertex velocities by removing, or filtering out, this spurious vorticity, rather than by the more common practice of introducing artificial viscosity. The first method reconstructs the velocity from the known flow divergence and from the true vorticity computed by means of a transport equation. The second method, which is much simpler and more efficient, subtracts a divergence-free correction from the velocity, such that the resulting velocity possesses the correct vorticity. We then successfully apply this method to solve a two-dimensional shock refraction problem, a problem which exhibits nonzero intrinsic vorticity.