The k-epsilon model in the theory of turbulence
We consider the $k-varepsilon$ model in the theory of turbulence, where $k$ is the turbulent kinetic energy, $varepsilon$ is the
dissipation rate of the turbulent energy, and $alpha,$ $eta,$ and $gamma$ are positive constants.
In particular we examine the Barenblatt self-similar $k-varepsilon$ model, along with boundary conditions taken to ensure the symmetry and compactness of the support of solutions.
Under the assumptions:
$eta>alpha,$ $3alpha>2eta,$ and $gamma$>3/2,
we show the existence of $mu$ for which there is a positive solution
to the system and corresponding boundary conditions by proving a series
of lemmas. We also include graphs of solutions obtained by using XPPAUT 5.85.
Advisor:J. Bryce McLeod; Stuart Hastings; Thomas Metzger; Peter Bushell
School:University of Pittsburgh
School Location:USA - Pennsylvania
Source Type:Master's Thesis
Date of Publication:01/31/2005