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Volume 4, Issue 3-4
Numerical Analysis of a Higher Order Time Relaxation Model of Fluids

V. J. Ervin, W. J. Layton & M. Neda

Int. J. Numer. Anal. Mod., 4 (2007), pp. 648-670.

Published online: 2007-04

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  • Abstract

We study the numerical errors in finite elements discretizations of a time relaxation model of fluid motion:
                          $u_t + u\cdot \nabla u + \nabla p - \nu\Delta u + \chi u^* = f$ and $\nabla \cdot u = 0$
In this model, introduced by Stolz, Adams, and Kleiser, $u^*$ is a generalized fluctuation and $\chi$ the time relaxation parameter. The goal of inclusion of the $\chi u^*$ is to drive unresolved fluctuations to zero exponentially. We study convergence of discretization of model to the model's solution as $h$, $\Delta t \rightarrow 0$. Next we complement this with an experimental study of the effect the time relaxation term (and a nonlinear extension of it) has on the large scales of a flow near a transitional point. We close by showing that the time relaxation term does not alter shock speeds in the inviscid, compressible case, giving analytical confirmation of a result of Stolz, Adams, and Kleiser.

  • Keywords

time relaxation, deconvolution, turbulence.

  • AMS Subject Headings

65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-4-648, author = {}, title = {Numerical Analysis of a Higher Order Time Relaxation Model of Fluids}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2007}, volume = {4}, number = {3-4}, pages = {648--670}, abstract = {

We study the numerical errors in finite elements discretizations of a time relaxation model of fluid motion:
                          $u_t + u\cdot \nabla u + \nabla p - \nu\Delta u + \chi u^* = f$ and $\nabla \cdot u = 0$
In this model, introduced by Stolz, Adams, and Kleiser, $u^*$ is a generalized fluctuation and $\chi$ the time relaxation parameter. The goal of inclusion of the $\chi u^*$ is to drive unresolved fluctuations to zero exponentially. We study convergence of discretization of model to the model's solution as $h$, $\Delta t \rightarrow 0$. Next we complement this with an experimental study of the effect the time relaxation term (and a nonlinear extension of it) has on the large scales of a flow near a transitional point. We close by showing that the time relaxation term does not alter shock speeds in the inviscid, compressible case, giving analytical confirmation of a result of Stolz, Adams, and Kleiser.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/882.html} }
TY - JOUR T1 - Numerical Analysis of a Higher Order Time Relaxation Model of Fluids JO - International Journal of Numerical Analysis and Modeling VL - 3-4 SP - 648 EP - 670 PY - 2007 DA - 2007/04 SN - 4 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/882.html KW - time relaxation, deconvolution, turbulence. AB -

We study the numerical errors in finite elements discretizations of a time relaxation model of fluid motion:
                          $u_t + u\cdot \nabla u + \nabla p - \nu\Delta u + \chi u^* = f$ and $\nabla \cdot u = 0$
In this model, introduced by Stolz, Adams, and Kleiser, $u^*$ is a generalized fluctuation and $\chi$ the time relaxation parameter. The goal of inclusion of the $\chi u^*$ is to drive unresolved fluctuations to zero exponentially. We study convergence of discretization of model to the model's solution as $h$, $\Delta t \rightarrow 0$. Next we complement this with an experimental study of the effect the time relaxation term (and a nonlinear extension of it) has on the large scales of a flow near a transitional point. We close by showing that the time relaxation term does not alter shock speeds in the inviscid, compressible case, giving analytical confirmation of a result of Stolz, Adams, and Kleiser.

V. J. Ervin, W. J. Layton & M. Neda. (1970). Numerical Analysis of a Higher Order Time Relaxation Model of Fluids. International Journal of Numerical Analysis and Modeling. 4 (3-4). 648-670. doi:
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