COMPARISON BETWEEN A CENTERED AND A HIGH RESOLUTION UPWIND SCHEMES IN THE SOLUTION OF AEROSPACE PROBLEMS USING UNSTRUCTURED STRATEGY Edisson Sávio de Góes Maciel Rua Demócrito Cavalcanti, 152 - Afogados Recife – PE – Brazil - CEP 50750-080 e-mail: edissonsavio@yahoo.com.br Abstract. The present work performs a comparison between a centered numerical scheme and a high resolution upwind scheme. The Jameson and Mavriplis algorithm, on the context of a centered spatial discretization and second order spatial accuracy, and the Frink, Parikh and Pirzadeh algorithm, on the context of upwind spatial discretization, using a flux difference splitting formulation and first order spatial accuracy, both explicit in time, are studied. The Jameson and Mavriplis algorithm uses an artificial dissipation operator to guarantee numerical stability. The Euler equations in conservative form, using a finite volume formulation and an unstructured spatial discretization of the flow equations, in two-dimensions, are solved. The transonic flow around a NACA 0012 airfoil and the supersonic flow around a simplified configuration of VLS are physical problems studied in this work. Both problems are studied in steady state regime and a zero angle of attack is adopted. The time integration uses a Runge-Kutta time stepping method of five stages and second order of accuracy. Results have shown good agreement between the algorithms with better solution quality characteristics and convergence acceleration properties to the Jameson and Mavriplis scheme. Keywords: Unstructured algorithms, Centered and high resolution upwind algorithms, Euler equations, Finite volume method, Aerospace problems. 1. Introduction The necessity of practical tests in several aerodynamics components of airplanes and aerospace vehicles during the project phase, in aeronautical and aerospace industries, is limited by the expensive cost due to the construction of scaled models and to perform tests in wind tunnels. Other main difficulties are related to the high number of experimental tests required during the optimization phase of these models. The development of computer technology, allowing the existence of high speed processors and high store capability, has boomed Computational Fluid Dynamics, CFD, towards to a meaningful role in several industry areas. Such areas require low cost levels during the experimental development and high performance of their products. In this work, the Jameson and Mavriplis (1986) and the Frink, Parikh and Pirzadeh (1991) explicit schemes, the last one using the flux difference splitting of Roe (1981), are compared using a finite volume formulation, based on a cell centered data base. The Jameson and Mavriplis (1986) scheme is really the most employed algorithm in terms of unstructured discretization of the fluid movement equations (Mavriplis and Jameson, 1987, Batina, 1990, Arnone, Liou and Povinelli, 1991, Long, Khan and Sharp, 1991, Swanson and Radespiel, 1991, and Hooker, Batina and Williams, 1992). The Frink, Parikh and Pirzadeh (1991) is a high resolution upwind scheme and presents good robustness properties (Frink, 1992, and Liou, Baum and Löhner, 1994). This comparison intends to emphasize important aspects of these algorithms in relation to: computational performance and some aspects of solution quality The physical problems of the transonic flow around a NACA 0012 airfoil and the supersonic flow around a simplified version of VLS configuration are studied using an unstructured discretization of the flow equations. An unstructured discretization of the spatial domain is often recommended to complex configurations due to the facility and efficiency of domain discretization (Jameson and Mavriplis, 1986, Mavriplis, 1990, Batina, 1990, and Pirzadeh, 1991). However, the unstructured generation question will not be studied in this work. The main objective of this work is to highlight the numerical features of the Jameson and Mavriplis (1986) and the Frink, Parikh and Pirzadeh (1991) schemes in the solution of the Euler equations, regardless of the method used for grid generation. 2. Euler equations The fluid movement is governed by the Euler equations, which express the mass, momentum and energy conservations of an inviscid, heat non-conductor and compressible mean, in the absence of external forces. In integral and conservative forms, these equations can be represented by: ( ) 0 dS n F n E QdV t S y e x e V = + + ∂ ∂ ∫ ∫ , (1)