Solutions of the Euler and the Laminar and Turbulent Navier-Stokes Equations in Two-Dimensions Using TVD and ENO Algorithms

摘要

In the present work, the Yee, Warming and Harten and the Yang schemes are implemented, on a finite volume context and using a structured spatial discretization, to solve the Euler and the Navier-Stokes equations in two-dimensions. The former is a TVD high resolution scheme, whereas the latter is an ENO/TVD high resolution algorithm. Both schemes are flux difference splitting ones. 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 models of Cebeci and Smith, of Baldwin and Lomax and of Sparlat and Allmaras. The physical problems of the transonic flow along a convergent-divergent nozzle and the supersonic flow along a compression corner are studied in the inviscid case. In the viscous case, the supersonic flow along a ramp is solved. The results have demonstrated that all three algorithms present accurate results.