First Order Unstructured Algorithms Applied to the Solution of the Euler Equations in Three-Dimensions

In the present work, the Roe, the Steger and Warming, the Van Leer, the Harten, the Frink, Parikh and Pirzadeh, the Liou and Steffen Jr. and the Radespiel and Kroll schemes are implemented, on a finite volume context and using an upwind and unstructured spatial discretization, to solve the Euler equations in the three-dimensional space. The Roe, the Harten, and the Frink, Parikh and Pirzadeh schemes are flux difference splitting ones, whereas the others schemes are flux vector splitting ones. All seven schemes are first order accurate in space. The time integration uses a Runge-Kutta method and is second order accurate. The physical problems of the supersonic flow along a ramp and the “cold gas” hypersonic flow along a diffuser are solved. The results have demonstrated that the Liou and Steffen Jr. scheme is the most conservative algorithm among the studied ones, whereas the Van Leer scheme is the most accurate. Key-Words: Flux difference splitting algorithms, Flux vector splitting algorithms, Unstructured schemes, Euler equations, Three-Dimensions, Supersonic and hypersonic flows.