WSEAS Transactions on Applied and Theoretical Mechanics
Print ISSN: 1991-8747, E-ISSN: 2224-3429
Volume 7, 2012
Explicit and Implicit TVD and ENO High Resolution Algorithms Applied to the Euler and Navier-Stokes Equations in Three-Dimensions – Turbulent Results
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Abstract: In the present work, the Harten and Osher TVD/ENO and the Yee TVD symmetric schemes are implemented, on a finite volume context and using a structured spatial discretization, to solve the laminar/turbulent Navier-Stokes equations in the three-dimensional space. The Harten and Osher TVD/ENO schemes are flux difference splitting type, whereas the Yee TVD scheme is a symmetric one, which incorporates TVD properties due to the appropriated definition of a limited dissipation function. All three schemes are second order accurate in space. Turbulence is taken into account considering two algebraic models, namely: the Cebeci and Smith and the Baldwin and Lomax ones. A spatially variable time step procedure is also implemented aiming to accelerate the convergence of the algorithms to the steady state solution. The gains in convergence with this procedure were demonstrated in Maciel. The schemes are applied to the solution of the physical problem of the low supersonic flow along a ramp. The results have demonstrated that the most accurate results are obtained with the Harten and Osher ENO scheme. This paper is the third part of this work, TURBULENT RESULTS, considering the description of the turbulence models and the solutions obtained with them and compared with the laminar results.
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Keywords: Harten and Osher algorithm, TVD/ENO formulations, Yee symmetric algorithm, TVD formulation, Euler and Navier-Stokes equations, Turbulence models, Explicit and implicit algorithms, Finite Volumes