Volume 26, Issue 2
A Targeted ENO Scheme as Implicit Model for Turbulent and Genuine Subgrid Scales

Lin Fu, Xiangyu Hu & Nikolaus A. Adams

Commun. Comput. Phys., 26 (2019), pp. 311-345.

Published online: 2019-04

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  • Abstract

Even for state-of-the-art implicit LES (ILES) methods, where the truncation error acts as physically-motivated subgrid-scale model, simultaneously resolving turbulent and genuine non-turbulent subgrid scales is an open challenge. For the purpose of dealing with non-turbulent subgrid scales, such as shocks, extra sensors, which often are case-dependent, are generally employed. The problem originates in the lack of scale-separation between low-wavenumber resolved-scale regions, high-wavenumber resolved or non-resolved fluctuations, and discontinuities. The targeted ENO (TENO) approach allows for separately designing the dispersive and dissipative truncation error components. Thus it provides a suitable environment to develop an implicit LES model. In this paper, we extend previous work and propose a variant of TENO family scheme [Fu et al., JCP 305 (2016): 333-359], which can separate resolved and nonresolved scales effectively. The novel idea is to propose a nonlinear dissipation-control strategy by adapting the cut-off parameter CT dynamically while measuring the nonsmoothness based on the first-order undivided difference. Low-wavenumber smooth scales are handled by an optimized linear scheme while high-wavenumber components, that involve nonresolved fluctuations and discontinuities, are subjected to adaptive nonlinear dissipation. A set of benchmark simulations with a wide range of length-scales and with discontinuities has been conducted without specific parameter adaptation. Numerical experiments demonstrate that the proposed TENO8-A scheme exhibits robust shock-capturing and high wave-resolution properties, and that it is suitable for simulating flow fields that contain isotropic turbulence and shocks. It is a promising alternative to other viable approaches.

  • Keywords

TENO scheme, high-order scheme, gas dynamics, turbulence, large-eddy simulation.

  • AMS Subject Headings

35L65, 65M06, 76J20, 76N15, 76F05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-26-311, author = {}, title = {A Targeted ENO Scheme as Implicit Model for Turbulent and Genuine Subgrid Scales}, journal = {Communications in Computational Physics}, year = {2019}, volume = {26}, number = {2}, pages = {311--345}, abstract = {

Even for state-of-the-art implicit LES (ILES) methods, where the truncation error acts as physically-motivated subgrid-scale model, simultaneously resolving turbulent and genuine non-turbulent subgrid scales is an open challenge. For the purpose of dealing with non-turbulent subgrid scales, such as shocks, extra sensors, which often are case-dependent, are generally employed. The problem originates in the lack of scale-separation between low-wavenumber resolved-scale regions, high-wavenumber resolved or non-resolved fluctuations, and discontinuities. The targeted ENO (TENO) approach allows for separately designing the dispersive and dissipative truncation error components. Thus it provides a suitable environment to develop an implicit LES model. In this paper, we extend previous work and propose a variant of TENO family scheme [Fu et al., JCP 305 (2016): 333-359], which can separate resolved and nonresolved scales effectively. The novel idea is to propose a nonlinear dissipation-control strategy by adapting the cut-off parameter CT dynamically while measuring the nonsmoothness based on the first-order undivided difference. Low-wavenumber smooth scales are handled by an optimized linear scheme while high-wavenumber components, that involve nonresolved fluctuations and discontinuities, are subjected to adaptive nonlinear dissipation. A set of benchmark simulations with a wide range of length-scales and with discontinuities has been conducted without specific parameter adaptation. Numerical experiments demonstrate that the proposed TENO8-A scheme exhibits robust shock-capturing and high wave-resolution properties, and that it is suitable for simulating flow fields that contain isotropic turbulence and shocks. It is a promising alternative to other viable approaches.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0145}, url = {http://global-sci.org/intro/article_detail/cicp/13094.html} }
TY - JOUR T1 - A Targeted ENO Scheme as Implicit Model for Turbulent and Genuine Subgrid Scales JO - Communications in Computational Physics VL - 2 SP - 311 EP - 345 PY - 2019 DA - 2019/04 SN - 26 DO - http://doi.org/10.4208/cicp.OA-2018-0145 UR - https://global-sci.org/intro/article_detail/cicp/13094.html KW - TENO scheme, high-order scheme, gas dynamics, turbulence, large-eddy simulation. AB -

Even for state-of-the-art implicit LES (ILES) methods, where the truncation error acts as physically-motivated subgrid-scale model, simultaneously resolving turbulent and genuine non-turbulent subgrid scales is an open challenge. For the purpose of dealing with non-turbulent subgrid scales, such as shocks, extra sensors, which often are case-dependent, are generally employed. The problem originates in the lack of scale-separation between low-wavenumber resolved-scale regions, high-wavenumber resolved or non-resolved fluctuations, and discontinuities. The targeted ENO (TENO) approach allows for separately designing the dispersive and dissipative truncation error components. Thus it provides a suitable environment to develop an implicit LES model. In this paper, we extend previous work and propose a variant of TENO family scheme [Fu et al., JCP 305 (2016): 333-359], which can separate resolved and nonresolved scales effectively. The novel idea is to propose a nonlinear dissipation-control strategy by adapting the cut-off parameter CT dynamically while measuring the nonsmoothness based on the first-order undivided difference. Low-wavenumber smooth scales are handled by an optimized linear scheme while high-wavenumber components, that involve nonresolved fluctuations and discontinuities, are subjected to adaptive nonlinear dissipation. A set of benchmark simulations with a wide range of length-scales and with discontinuities has been conducted without specific parameter adaptation. Numerical experiments demonstrate that the proposed TENO8-A scheme exhibits robust shock-capturing and high wave-resolution properties, and that it is suitable for simulating flow fields that contain isotropic turbulence and shocks. It is a promising alternative to other viable approaches.

Lin Fu, Xiangyu Hu & Nikolaus A. Adams. (2019). A Targeted ENO Scheme as Implicit Model for Turbulent and Genuine Subgrid Scales. Communications in Computational Physics. 26 (2). 311-345. doi:10.4208/cicp.OA-2018-0145
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