Volume 15, Issue 6
Model Error in the LANS-Alpha and NS-Alpha Deconvolution Models of Turbulence

Int. J. Numer. Anal. Mod., 15 (2018), pp. 811-833.

Published online: 2018-08

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• Abstract

This paper reports on a computational study of the model error in the LANS-alpha and NS-alpha deconvolution models of homogeneous isotropic turbulence. Computations are also performed for a new turbulence model obtained as a rescaled limit of the deconvolution model. The technique used is to plug a solution obtained from direct numerical simulation of the incompressible Navier–Stokes equations into the competing turbulence models and to then compute the time evolution of the resulting residual. All computations have been done in two dimensions rather than three for convenience and efficiency. When the effective averaging length scale in any of the models is $α_0 = 0.01$, the time evolution of the root-mean-squared residual error grows as $\sqrt{t}$. This growth rate similar to what would happen if the model error were given by a stochastic force. When $α_0 = 0.20$, the residual error grows linearly. Linear growth suggests that the model error possesses a systematic bias. Finally, for $α_0 = 0.04$, the residual error in LANS-alpha model exhibited linear growth; however, for this value of $α_0$, the higher-order alpha models that were tested did not.

• Keywords

Alpha-model, bias, model error, Navier-Stokes, stochastic force.

37L55, 65C20, 65N12, 65P20, 76F05

ejolson@unr.edu (Eric Olson)

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@Article{IJNAM-15-811, author = {Olson , Eric}, title = {Model Error in the LANS-Alpha and NS-Alpha Deconvolution Models of Turbulence}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {15}, number = {6}, pages = {811--833}, abstract = {

This paper reports on a computational study of the model error in the LANS-alpha and NS-alpha deconvolution models of homogeneous isotropic turbulence. Computations are also performed for a new turbulence model obtained as a rescaled limit of the deconvolution model. The technique used is to plug a solution obtained from direct numerical simulation of the incompressible Navier–Stokes equations into the competing turbulence models and to then compute the time evolution of the resulting residual. All computations have been done in two dimensions rather than three for convenience and efficiency. When the effective averaging length scale in any of the models is $α_0 = 0.01$, the time evolution of the root-mean-squared residual error grows as $\sqrt{t}$. This growth rate similar to what would happen if the model error were given by a stochastic force. When $α_0 = 0.20$, the residual error grows linearly. Linear growth suggests that the model error possesses a systematic bias. Finally, for $α_0 = 0.04$, the residual error in LANS-alpha model exhibited linear growth; however, for this value of $α_0$, the higher-order alpha models that were tested did not.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/12610.html} }
TY - JOUR T1 - Model Error in the LANS-Alpha and NS-Alpha Deconvolution Models of Turbulence AU - Olson , Eric JO - International Journal of Numerical Analysis and Modeling VL - 6 SP - 811 EP - 833 PY - 2018 DA - 2018/08 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/12610.html KW - Alpha-model, bias, model error, Navier-Stokes, stochastic force. AB -

This paper reports on a computational study of the model error in the LANS-alpha and NS-alpha deconvolution models of homogeneous isotropic turbulence. Computations are also performed for a new turbulence model obtained as a rescaled limit of the deconvolution model. The technique used is to plug a solution obtained from direct numerical simulation of the incompressible Navier–Stokes equations into the competing turbulence models and to then compute the time evolution of the resulting residual. All computations have been done in two dimensions rather than three for convenience and efficiency. When the effective averaging length scale in any of the models is $α_0 = 0.01$, the time evolution of the root-mean-squared residual error grows as $\sqrt{t}$. This growth rate similar to what would happen if the model error were given by a stochastic force. When $α_0 = 0.20$, the residual error grows linearly. Linear growth suggests that the model error possesses a systematic bias. Finally, for $α_0 = 0.04$, the residual error in LANS-alpha model exhibited linear growth; however, for this value of $α_0$, the higher-order alpha models that were tested did not.

Eric Olson. (2020). Model Error in the LANS-Alpha and NS-Alpha Deconvolution Models of Turbulence. International Journal of Numerical Analysis and Modeling. 15 (6). 811-833. doi:
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