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

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

DOI:

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 center dot del u + del(p) - nu del u + chi u* = f and del center dot u = 0
In this model, introduced by Stolz, Adams, and Kleisser, 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 sero exponentially. We study convergence of discretization of model to the model's solution as h, Delta t -> 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 = {V. J. Ervin, W. J. Layton and M. Neda}, 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 center dot del u + del(p) - nu del u + chi u* = f and del center dot u = 0
In this model, introduced by Stolz, Adams, and Kleisser, 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 sero exponentially. We study convergence of discretization of model to the model's solution as h, Delta t -> 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 AU - V. J. Ervin, W. J. Layton & M. Neda JO - International Journal of Numerical Analysis and Modeling VL - 3-4 SP - 648 EP - 670 PY - 2007 DA - 2007/04 SN - 4 DO - http://dor.org/ UR - https://global-sci.org/intro/article_detail/ijnam/882.html KW - time relaxation KW - deconvolution KW - turbulence AB - We study the numerical errors in finite elements discretizations of a time relaxation model of fluid motion:
u(t) + u center dot del u + del(p) - nu del u + chi u* = f and del center dot u = 0
In this model, introduced by Stolz, Adams, and Kleisser, 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 sero exponentially. We study convergence of discretization of model to the model's solution as h, Delta t -> 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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