TVD and ENO Applications to Supersonic Flows in 2D - Part II

摘要

In this work, second part of this study, the high resolution numerical schemes of Yee and Harten, of Yang second order, of Yang third order, and of Yang and Hsu are applied to the solution of the Euler and Navier-Stokes equations in two-dimensions. All schemes are flux difference splitting algorithms. The Yee and Harten is a TVD ("Total Variation Diminishing") second order accurate in space and first order accurate in time algorithm. The Yang second order is a TVD/ENO ("Essentially Nonoscillatory") second order accurate in space and first order accurate in time algorithm. The Yang third order is a TVD/ENO third order accurate in space and first order accurate in time algorithm. Finally, the Yang and Hsu is a UNO (Uniformly Nonoscillatory) third order accurate in space and first order accurate in time algorithm. The Euler and Navier-Stokes equations, written in a conservative and integral form, are solved, according to a finite volume and structured formulations. A spatially variable time step procedure is employed aiming to accelerate the convergence of the numerical schemes to the steady state condition. It has proved excellent gains in terms of convergence acceleration as reported by Maciel. The physical problems of the supersonic shock reflection at the wall and the supersonic flow along a compression corner are solved, in the inviscid case. For the viscous case, the supersonic flow along a compression corner is solved. In the inviscid case, an implicit formulation is employed to marching in time, whereas in the viscous case, a time splitting or Strang approaches are used. The results have demonstrated that the Yang ENO third order accurate algorithm has presented the best solutions in the problems studied herein. Moreover, it is also the best as comparing with the numerical schemes of Part I of this study.