Balancing aspects of numerical dissipation, dispersion, and aliasing in time‐accurate simulations,International Journal for Numerical Methods in Fluids

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Balancing aspects of numerical dissipation, dispersion, and aliasing in time‐accurate simulations
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2020-04-06 , DOI: 10.1002/fld.4837
Ayaboe K. Edoh _{1,

2,

3} , Nathan L. Mundis ₂ , Ann R. Karagozian ₃ , Venkateswaran Sankaran ₄

Affiliation

The current study looks at the selection of scheme elements that are well‐suited for long‐time integration of unsteady flows in the absence or under‐resolution of physical diffusion. A concerted assembly of numerical components are chosen relative to a target aliasing limit, which is taken as a best‐case scenario for overall spectral resolvability. High‐order and optimized difference stencils are employed in order to achieve accuracy; meanwhile, quasi skew‐symmetric splitting techniques for nonlinear transport terms are used in order to greatly improve robustness. Finally, tunable and scale‐discriminant artificial‐dissipation methods are incorporated for de‐aliasing purposes and as a means of further enhancing both accuracy and stability. Central finite difference methods are considered, and spectral characterizations of the scheme components are presented. Canonical test cases (the isentropic vortex [IV] and Taylor‐Green vortex problems) are chosen in order to highlight the benefits associated with the proposed approach for enhancing overall algorithm robustness and accuracy.

中文翻译：

在时间精确的仿真中平衡数值耗散，色散和混叠的方面

当前的研究着眼于在物理扩散不存在或分辨率较低的情况下，非常适合于非定常流长期集成的方案元素的选择。相对于目标混叠极限，选择了协调一致的数字分量集合，这被视为总体光谱可分辨性的最佳方案。使用高阶和优化的差异模具以实现准确性；同时，为非线性传输项使用准偏斜对称分裂技术以大大提高鲁棒性。最后，为了消除混叠的目的并结合了可调谐和规模微分的人工耗散方法，这是进一步提高准确性和稳定性的一种手段。考虑了中心有限差分法，并给出了方案组成的光谱表征。选择典型的测试用例（等熵涡旋[IV]和Taylor-Green涡旋问题），以突出与建议的方法相关的好处，以增强整体算法的鲁棒性和准确性。

更新日期：2020-04-06

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