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://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/882.html
KW - time relaxation, deconvolution, turbulence.
AB - <p style="text-align: justify;">We study the numerical errors in finite elements
discretizations of a time relaxation model of fluid motion:<br/>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; $u_t + u\cdot \nabla u + \nabla p - \nu\Delta u + \chi u^* = f$ and $\nabla \cdot u = 0$<br/>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&#39;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.</p>