p-version least-squares finite element formulation of extendedk-? model of turbulence for fully developed flow

✍ Scribed by Bagheri, Masoud ;Surana, Karan S.

• Publisher: John Wiley and Sons
• Year: 2000
• Tongue: English
• Weight: 127 KB
• Volume: 16
• Category: Article
• ISSN: 1069-8299
• DOI: 10.1002/(sici)1099-0887(200002)16:2<83::aid-cnm311>3.0.co;2-l

✦ Synopsis

This paper presents a p-version least-squares "nite element formulation for an extended k} turbulence model. The dimensionless form of the describing partial di!erential equations are cast into a system of "rst-order partial di!erential equations by utilizing auxiliary variables. Primary, and auxiliary variables are interpolated over an element using equal order C equal order p-version hierarchical interpolation functions. The least-squares error functional is constructed by taking the integrated sum of squares of the errors resulting from the system of "rst-order equations for the entire discretization. The minimization of this least-squares error functional results in "nding a solution vector + , for which the partial derivative of the error functional, with respect to nodal degrees of freedom + ,, becomes zero. This is accomplished by using Newton's method with line search. Numerical examples are presented for fully developed one-dimensional turbulent channel #ow utilizing the k} model of Launder and Sharma for various Reynolds numbers to demonstrate the convergence characteristics and accuracy of the proposed formulation. Our converged numerical solutions are in very good agreement with the computed results reported by other researchers. The formulation presented here enjoys all of the bene"ts of least-squares approach for highly non-linear and non-elliptic partial di!erential equations over Galerkin methods.