TVD Algorithms Applied to the Solution of the Euler and Navier-Stokes Equations in Three-Dimensions

摘要

In the present work, the Yee, Warming and Harten, the Harten, the Yee and Kutler, and the Hughson and Beran 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. All four schemes are TVD ("Total Variation Diminishing") high resolution flux difference splitting ones, second order accurate. An implicit formulation is employed to solve the Euler equations, whereas the Navier-Stokes equations are solved by an explicit formulation. Turbulence is taken into account considering the algebraic models of Cebeci and Smith and of Baldwin and Lomax. The physical problems of the transonic flow along a convergent-divergent nozzle and the supersonic flow along a compression corner in the inviscid case are studied. In the viscous case, the supersonic flow along a ramp is solved. The results have demonstrated that the most severe results are obtained with the Hughson and Beran TVD high resolution scheme, whereas the Yee, Wanning and Harten and the Yee and Kutler schemes present more accurate results.