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<p>In this work, an <i>a priori</i> investigation of a novel family of subgrid scale (SGS) models for the large eddy simulation (LES) is presented. This family of models has the particularity to preserve the Lie-symmetries of the incompressible Navier-Stokes equations. The <i>a priori</i> tests are conducted on the numerical results of a (forced) homogeneous, isotropic and turbulent (HIT) flow which are available in the John Hopkins’ database (JHTDB). In addition to the new family of invariant models, several established subgrid scale models, including scale similarity models, eddy viscosity models and a non linear model are considered for comparison. The accuracy and performance of the models are quantified using the correlation coefficient between the reference subgrid scale tensor and the models. Both box and spectral filters are considered with different filter sizes. The energy dissipation is also evaluated to assess the capability of the models to correctly capture the energy-transfer between the resolved and the unresolved scales. The general invariant model is found to behave similarly to the non linear model of Lund and Novikov, yielding a correlation coefficient of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\eta = 0.8\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>η</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </math></EquationSource> </InlineEquation> at small filter widths. Moreover, it closely matches the true subgrid scale dissipation and accounts for backscatter.</p>

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A priori analysis of subgrid scale models that preserve the Lie-symmetries of the Navier–Stokes equations for large eddy simulations

  • 期刊论文

  • 发表日期：

    2026年3月17日

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  • Nadjma Akhal,
  • Can Selçuk,
  • Stéphane Vincent,
  • Benoît Trouette

摘要

In this work, an a priori investigation of a novel family of subgrid scale (SGS) models for the large eddy simulation (LES) is presented. This family of models has the particularity to preserve the Lie-symmetries of the incompressible Navier-Stokes equations. The a priori tests are conducted on the numerical results of a (forced) homogeneous, isotropic and turbulent (HIT) flow which are available in the John Hopkins’ database (JHTDB). In addition to the new family of invariant models, several established subgrid scale models, including scale similarity models, eddy viscosity models and a non linear model are considered for comparison. The accuracy and performance of the models are quantified using the correlation coefficient between the reference subgrid scale tensor and the models. Both box and spectral filters are considered with different filter sizes. The energy dissipation is also evaluated to assess the capability of the models to correctly capture the energy-transfer between the resolved and the unresolved scales. The general invariant model is found to behave similarly to the non linear model of Lund and Novikov, yielding a correlation coefficient of \(\eta = 0.8\) η = 0.8 at small filter widths. Moreover, it closely matches the true subgrid scale dissipation and accounts for backscatter.