Noma Park

Analysis of numerical errors in large eddy simulation using statistical closure theory

This paper develops a dynamic error analysis procedure for the numerical errors arising from spatial discretization in large-eddy simulation. The analysis is based on EDQNM closure theory, and is applied to the LES of decaying isotropic turbulence. First, the effects of finite-differencing truncation error, aliasing error and the dynamic Smagorinsky model are independently considered. The time-evolution of kinetic energy and spectra predicted by the analysis are compared to actual LES using the Navier-Stokes equations, and good agreement is obtained. The analysis is then extended to simultaneously consider all sources of error in a second-order discretely energy conserving, central-difference LES solver. Good agreement between the analysis and actual LES is obtained. The analysis is used to compare the contribution of the subgrid model to that of numerical errors, and it is shown that the contribution of the subgrid scale model is much higher than the numerical errors. The proposed one-dimensional EDQNM-LES model shows potential as a more general tool for the analysis of numerical error, and SGS model in simulations of turbulent flow.

Reduction of the Germano-identity error in the dynamic Smagorinsky model

We revisit the Germano-identity error in the dynamic modeling procedure in the sense that the current modeling procedure to obtain the dynamic coefficient may not truly minimize the error in the mean and global sense. A “corrector step” to the conventional dynamic Smagorinsky model is proposed to obtain a corrected eddy viscosity which further reduces the error. The change in resolved velocity due to the coefficient variation as well as nonlocal nature of the filter and flow unsteadiness is accounted for by a simplified suboptimal control formalism without resorting to the adjoint equations. The objective function chosen is the Germano-identity error integrated over the entire computational volume and pathline. In order to determine corrected eddy viscosity, the Frechet derivative of the objective function is directly evaluated by a finite-differencing formula in an efficient predictor-corrector-type framework. The proposed model is applied to decaying isotropic turbulence and turbulent channel flow at va...

A velocity-estimation subgrid model constrained by subgrid scale dissipation

Purely dissipative eddy-viscosity subgrid models have proven very successful in large-eddy simulations (LES) at moderate resolution. Simulations at coarse resolutions where the underlying assumption of small-scale universality is not valid, warrant more advanced models. However, non-eddy viscosity models are often unstable due to the lack of sufficient dissipation. This paper proposes a simple modeling approach which incorporates the dissipative nature of existing eddy viscosity models into more physically appealing non-eddy viscosity SGS models. The key idea is to impose the SGS dissipation of the eddy viscosity model as a constraint on the non-eddy viscosity model when determining the coefficients in the non-eddy viscosity model. We propose a new subgrid scale model (RSEM), which is based on estimation of the unresolved velocity field. RSEM is developed in physical space and does not require the use of finer grids to estimate the subgrid velocity field. The model coefficient is determined such that total SGS dissipation matches that from a target SGS model in the mean or least-squares sense. The dynamic Smagorinsky model is used to provide the target dissipation. Results are shown for LES of decaying isotropic turbulence and turbulent channel flow. For isotropic turbulence, RSEM displays some level of backward dissipation, while yielding as good results as the dynamic Smagorinsky model. For channel flow, the results from RSEM are better than those from the dynamic Smagorinsky model for both statistics and instantaneous flow structures.

Numerical and modeling issues in LES of compressible turbulence on unstructured grids

This paper discusses numerical and modeling issues that arise in cell-centered flnitevolume methods (FVM) for large eddy simulation (LES) of compressible ∞ows on unstructured grids. These are: accuracy and stability of ∞ux interpolation scheme, shock capturing strategy, and subgrid-scale (SGS) modeling. To enhance the accuracy of ∞ux reconstruction, a new scheme with added flrst derivative term from each cell center is proposed, and tested for various benchmark problems. It is shown that stability as well as accuracy is determined by the formulation of gradient at cell center. As a shock-capturing method, a characteristic based fllter is formulated for cell-centered FVM on unstructured grids. The fllter is combined with a sensor based on the local divergence and vorticity. Also, a one-equation subgrid model based on the subgrid kinetic energy transport equation for compressible ∞ows is proposed.

A hybrid subgrid-scale model constrained by Reynolds stress

A novel constrained formulation for the dynamic subgrid-scale model for large eddy simulation (LES) is proposed. An externally prescribed Reynolds stress is used as the constraint and is imposed in the near-wall region of wall-bounded flows. However, unlike conventional zonal approaches, Reynolds stress is not imposed as the solution, but used as a constraint on the subgrid-scale stress so that the computed Reynolds stress closely matches the prescribed one only in the mean sense. In the absence of an ideal wall model or adequate near-wall resolution, a LES solution at coarse resolution is expected to be erroneous very near the wall while giving reasonable predictions away from the wall. The Reynolds stress constraint is limited to the region where the LES solution is expected to be erroneous. The Germano-identity error is used as an indicator of LES quality such that the Reynolds stress constraint is activated only where the Germano-identity error exceeds a certain threshold. The proposed model is applie...

A dynamic characteristic filter for DNS/LES of compressible turbulent flows

We propose a novel shock-capturing method that is based on the ideas of characteristic filters and dynamic suboptimal control. A cost function is based on the smoothness of the solution, and formally minimized to obtain the unknown coefficient in the shock-capturing numerical fluxes. The proposed dynamic procedure is applied to one–dimensional Euler equation equation and two–dimensional Navier–Stokes equation. The proposed dynamic filter achieved noticeable success in capturing shock while minimizing the overall impact on the solution.