Comparison Among Structured High Resolution Algorithms In The Solution Of The Euler Equations In Two-Dimensions.

Abstract

The present work compares the Yee, Warming and Harten, the Harten, the Yee and Kutler
and the Hughson and Beran high resolution schemes applied to the solution of aeronautical and
aerospace problems. All schemes are TVD flux difference splitting type and are second order accurate
in space. The Euler equations in conservative form, employing a finite volume formulation and a
structured spatial discretization, are solved in two-dimensions. The time integration is performed by a
time splitting method and is first order accurate. The steady state physical problems of the supersonic
flows along a ramp and around a blunt body configuration are studied. In the ramp problem, the
Hughson and Beran scheme was the most critical because presented the most severe pressure field and
the most intense Mach number field in relation to the others schemes. The shock and the expansion fan
are better captured by the Yee, Warming and Harten and the Yee and Kutler schemes. The Harten and
the Hughson and Beran schemes presented better pressure distribution than the others schemes when
compared with the theory. The shock angle was best estimated by the Harten scheme. In the blunt
body problem, the Harten scheme presented the most severe pressure field in relation to the others
schemes. The aerodynamic coefficient of lift was better estimated in the solutions generated by the
Harten and the Hughson and Beran schemes. The stagnation pressure ahead of the configuration is
best predicted by the Harten scheme. As conclusion, the Harten scheme presents the most accurate
solutions in comparison with the others schemes in both examples studied in this work, as well the
most severe pressure field in the blunt body problem, high supersonic flow, characterizing it as the
most conservative in relation to the others schemes to this type of flow, which indicates this one as a
good scheme to the prediction of flow properties in the project phase of aerospace vehicles.