Comparison among Unstructured TVD, ENO and UNO Schemes in Two-dimensions
Edisson Sávio de Góes Maciel *
Instituto Tecnológico de Aeronáutica (ITA), Rua Santa Clara, 245 – Cx. Postal: 2029 – 12.243-970, São José dos Campos, SP, Brazil.
Cláudia Regina de Andrade
Instituto Tecnológico de Aeronáutica (ITA), Praça Mal. Do Ar Eduardo Gomes, 50 – Vila das Acácias, São José dos Campos, SP, Brazil.
*Author to whom correspondence should be addressed.
Abstract
In this work, unstructured TVD, ENO and UNO schemes are applied to solve the Euler equations in two-dimensions. They are implemented on a finite volume context and cell centered data base. The algorithms of Yee, Warming and Harten 1982; Harten; Yee and Kutler; Yee Warming and Harten 1985; Yee; Yee and Harten; Harten and Osher; Yang; Hughson and Beran; and Yang and Hsu are implemented to solve such system of equations in two-dimensions. All schemes are flux difference splitting and good resolution is expected. This study deals with calorically perfect gas model and in so on the cold gas formulation is employed. Two problems are studied, namely: the transonic convergent-divergent symmetrical nozzle, and the supersonic ramp. A spatially variable time step is implemented to accelerate the convergence process. The results highlights the excellent performance of the Yang TVD scheme, yielding an excellent pressure distribution at the nozzle wall, whereas the Harten and Osher scheme yields accurate values to the angle of the oblique shock wave and the best wall pressure distributions in the ramp problem.
Keywords: Supersonic and transonic flow, Euler equations, TVD schemes, ENO schemes, UNO schemes, flux difference splitting, two-dimension, second and third-order schemes.