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- W2071044037 abstract "This paper presents a p-version least-squares finite element formulation for an extended k-e turbulence model. The dimensionless form of the describing partial differential equations are cast into a system of first-order partial differential 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 first-order equations for the entire discretization. The minimization of this least-squares error functional results in finding a solution vector {δ} for which the partial derivative of the error functional, with respect to nodal degrees of freedom {δ}, becomes zero. This is accomplished by using Newton's method with line search. Numerical examples are presented for fully developed one-dimensional turbulent channel flow utilizing the k-e 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 benefits of least-squares approach for highly non-linear and non-elliptic partial differential equations over Galerkin methods." @default.
- W2071044037 created "2016-06-24" @default.
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- W2071044037 date "2000-02-01" @default.
- W2071044037 modified "2023-09-27" @default.
- W2071044037 title "p-version least-squares finite element formulation of extendedk-? model of turbulence for fully developed flow" @default.
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- W2071044037 doi "https://doi.org/10.1002/(sici)1099-0887(200002)16:2<83::aid-cnm311>3.0.co;2-l" @default.
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