Year: 2007
International Journal of Numerical Analysis and Modeling, Vol. 4 (2007), Iss. 3-4 : pp. 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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2007-IJNAM-882
International Journal of Numerical Analysis and Modeling, Vol. 4 (2007), Iss. 3-4 : pp. 648–670
Published online: 2007-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: time relaxation deconvolution turbulence.