WSEAS Transactions on Applied and Theoretical Mechanics
Print ISSN: 1991-8747, E-ISSN: 2224-3429
Volume 7, 2012
TVD Flux Vector Splitting Algorithms Applied to the Solution of the Euler and Navier-Stokes Equations in Three-Dimensions – Part I
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Abstract: In the present work, the Steger and Warming, the Van Leer, the Liou and Steffen Jr. and the Radespiel and Kroll schemes are implemented, on a finite volume context and using a structured spatial discretization, to solve the Euler and the Navier-Stokes equations in three-dimensions. A MUSCL (“Monotone Upstream-centered Schemes for Conservation Laws”) approach is implemented in these schemes aiming to obtain second order spatial accuracy and TVD (“Total Variation Diminishing”) high resolution properties. An implicit formulation is employed to the Euler equations, whereas the Navier-Stokes equations use an explicit formulation. The algebraic turbulence models of Cebeci and Smith and of Baldwin and Lomax are implemented. The problems of the supersonic flow along a compression corner (inviscid case), and of the supersonic flow along a ramp (viscous case) are solved. The results have demonstrated that the most severe and most accurate results are obtained with the Liou and Steffen Jr. TVD scheme. The turbulent results are presented in the second part of this work.
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Keywords: Steger and Warming algorithm, Van Leer algorithm, Liou and Steffen Jr. algorithm, Radespiel and Kroll algorithm, TVD high resolution schemes, Turbulence models, Euler and Navier-Stokes equations, Three-Dimensions