基于强质心Lloyd网格正则化的动网格编码降噪
Reducing noise in moving-grid codes with strongly-centroidal Lloyd mesh regularization
摘要：
本文介绍了一种改进使用移动Voronoi网格的流体动力学代码精度的方法。我们的计划是基于一个新的正则化方案，约束网格的质心，以高精度，同时仍然允许细胞移动近似与当地的流体速度，从而保留了准拉格朗日性质的方法。我们的正则化技术显着减少网格噪声，这是由于网格拓扑结构的变化和网格规则性的偏差。我们证明了我们的方法在各种测试问题上的优势，并特别注意到在处理剪切不稳定性，混合和角动量守恒方面取得的改进。绝热射流中的剪切激发Kelvin Helmholtz不稳定性的计算表明，减少网格噪声和熵产生。相比之下，孤立盘星系的坍缩和形成的模拟几乎不受影响，这表明由于正则化的选择而导致的数值误差不会影响这种情况下的结果。
英文摘要：
A method for improving the accuracy of hydrodynamical codes that use a moving Voronoi mesh is described. Our scheme is based on a new regularization scheme that constrains the mesh to be centroidal to high precision while still allowing the cells to move approximately with the local fluid velocity, thereby retaining the quasi-Lagrangian nature of the approach. Our regularization technique significantly reduces mesh noise that is attributed to changes in mesh topology and deviations from mesh regularity. We demonstrate the advantages of our method on various test problems, and note in particular improvements obtained in handling shear instabilities, mixing, and in angular momentum conservation. Calculations of adiabatic jets in which shear excites Kelvin Helmholtz instability show reduction of mesh noise and entropy generation. In contrast, simulations of the collapse and formation of an isolated disc galaxy are nearly unaffected, showing that numerical errors due to the choice of regularization do not impact the outcome in this case.
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