Volume 21, Issue 1
A Mathematical Analysis of Scale Similarity

Commun. Comput. Phys., 21 (2017), pp. 149-161.

Published online: 2018-04

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• Abstract

Scale similarity is found in many natural phenomena in the universe, from fluid dynamics to astrophysics. In large eddy simulations of turbulent flows, some sub-grid scale (SGS) models are based on scale similarity. The earliest scale similarity SGS model was developed by Bardina et al., which produced SGS stresses with good correlation to the true stresses. In the present study, we perform a mathematical analysis of scale similarity. The analysis has revealed that the ratio of the resolved stress to the SGS stress is $γ^2$ , where $γ$ is the ratio of the second filter width to the first filter width, under the assumption of small filter width. The implications of this analysis are discussed in the context of large eddy simulation.

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@Article{CiCP-21-149, author = {}, title = {A Mathematical Analysis of Scale Similarity}, journal = {Communications in Computational Physics}, year = {2018}, volume = {21}, number = {1}, pages = {149--161}, abstract = {

Scale similarity is found in many natural phenomena in the universe, from fluid dynamics to astrophysics. In large eddy simulations of turbulent flows, some sub-grid scale (SGS) models are based on scale similarity. The earliest scale similarity SGS model was developed by Bardina et al., which produced SGS stresses with good correlation to the true stresses. In the present study, we perform a mathematical analysis of scale similarity. The analysis has revealed that the ratio of the resolved stress to the SGS stress is $γ^2$ , where $γ$ is the ratio of the second filter width to the first filter width, under the assumption of small filter width. The implications of this analysis are discussed in the context of large eddy simulation.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.131015.110416a}, url = {http://global-sci.org/intro/article_detail/cicp/11235.html} }
TY - JOUR T1 - A Mathematical Analysis of Scale Similarity JO - Communications in Computational Physics VL - 1 SP - 149 EP - 161 PY - 2018 DA - 2018/04 SN - 21 DO - http://doi.org/10.4208/cicp.131015.110416a UR - https://global-sci.org/intro/article_detail/cicp/11235.html KW - AB -

Scale similarity is found in many natural phenomena in the universe, from fluid dynamics to astrophysics. In large eddy simulations of turbulent flows, some sub-grid scale (SGS) models are based on scale similarity. The earliest scale similarity SGS model was developed by Bardina et al., which produced SGS stresses with good correlation to the true stresses. In the present study, we perform a mathematical analysis of scale similarity. The analysis has revealed that the ratio of the resolved stress to the SGS stress is $γ^2$ , where $γ$ is the ratio of the second filter width to the first filter width, under the assumption of small filter width. The implications of this analysis are discussed in the context of large eddy simulation.

Z. J. Wang & Yanan Li. (2020). A Mathematical Analysis of Scale Similarity. Communications in Computational Physics. 21 (1). 149-161. doi:10.4208/cicp.131015.110416a
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