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:
ut+u⋅∇u+∇p−νΔu+χu∗=f and ∇⋅u=0
In this model, introduced by Stolz, Adams, and Kleiser, u∗ is a
generalized fluctuation and χ the time relaxation parameter. The goal
of inclusion of the χu∗ is to drive unresolved fluctuations to zero
exponentially. We study convergence of discretization of model to the
model's solution as h, Δt→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.
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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.