5 research outputs found
An assessment of unstructured grid finite volume schemes for cold gas hypersonic flow calculations
A comparison of five different spatial discretization schemes is performed considering a typical high speed flow application. Flowfields are simulated using the 2-D Euler equations, discretized in a cell-centered finite volume procedure on unstructured triangular meshes. The algorithms studied include a central difference-type scheme, and 1st- and 2nd-order van Leer and Liou flux-vector splitting schemes. These methods are implemented in an efficient, edge-based, unstructured grid procedure which allows for adaptive mesh refinement based on flow property gradients. Details of the unstructured grid implementation of the methods are presented together with a discussion of the data structure and of the adaptive refinement strategy. The application of interest is the cold gas flow through a typical hypersonic inlet. Results for different entrance Mach numbers and mesh topologies are discussed in order to assess the comparative performance of the various spatial discretization schemes
An study about solving equations of interval coefficients
O objetivo deste trabalho e determinar a soluĆ§Ć£o de algumas equaƧƵes de coeficientes intervalares. Este estudo utiliza uma Teoria das AproximaƧƵes Intervalares, a qual foi descrita por [ACI91]. Nesta teoria a igualdade para intervalos e substituĆda pela relaĆ§Ć£o de aproximaĆ§Ć£o . Esta substituiĆ§Ć£o deve-se ao fato da igualdade utilizada na Teoria ClĆ”ssica dos Intervalos para resoluĆ§Ć£o de equaƧƵes de coeficientes intervalares nĆ£o apresentar uma soluĆ§Ć£o satisfatĆ³ria, visto que a soluĆ§Ć£o encontrada nĆ£o contem todas as soluƧƵes das equaƧƵes reais que compƵe a equaĆ§Ć£o intervalar. Pela substituiĆ§Ć£o da igualdade intervalar por uma relaĆ§Ć£o de aproximaĆ§Ć£o Ć© possĆvel determinar a soluĆ§Ć£o de equaƧƵes de coeficientes intervalares, de maneira que esta soluĆ§Ć£o contenha todas as possĆveis soluƧƵes das equaƧƵes reais pertencentes a equaĆ§Ć£o intervalar. Apresenta-se alguns conceitos bĆ”sicos, bem como analisa-se algumas propriedades no espaƧo soluĆ§Ć£o ( /(R), +, ā¢, C, 1). SĆ£o representadas graficamente diferentes tipos de funƧƵes neste espaƧo intervalar, com os objetivos de obtenĆ§Ć£o da imagem, caracterizaĆ§Ć£o da soluĆ§Ć£o e identificaĆ§Ć£o grĆ”fica da regiĆ£o de soluĆ§Ć£o (Ć³tima e externa), para cada tipo de funĆ§Ć£o. Como a representaĆ§Ć£o de intervalos de /(R) esta determinada num semiplano de eixos X - X+, onde X - representa o extremo inferior de cada intervalo e X+ representa o extremo superior dos intervalos, apresenta-se o espaƧo intervalar estendido /(R). Neste espaƧo intervalar estĆ£o definidos os intervalos nĆ£o-regulares, representados no outro semi-piano de eixos X - X+ Em /(R) serĆ£o apresentados alguns conceitos fundamentais, assim como operaƧƵes aritmĆ©ticas e algumas consideraƧƵes referentes aos intervalos nĆ£o-regulares. No espaƧo intervalar /(R) e possĆvel resolver equaƧƵes de coeficientes intervalares de maneira anĆ”loga a resoluĆ§Ć£o de equaƧƵes reais no espaƧo real, pois este espaƧo intervalar possui a estrutura semelhante a de um corpo. Com isto apresenta-se a soluĆ§Ć£o de equaƧƵes de coeficientes intervalares lineares, obtida diretamente, assim como determina-se a Formula de Bascara Intervalar para resoluĆ§Ć£o da EquaĆ§Ć£o QuadrĆ”tica Intervalar. Para funƧƵes que possuem grau maior que 2 apresenta-se alguns mĆ©todos iterativos intervalares, tais como o MĆ©todo de Newton Intervalar, o MĆ©todo da Secante Intervalar e o MĆ©todo hĆbrido Intervalar, que permitem a obtenĆ§Ć£o do intervalo soluĆ§Ć£o para funƧƵes intervalares. Por fim apresenta-se alguns conceitos bĆ”sicos no espaƧo intervalar matricial Mā,ā(/(R)), bem como apresenta-se alguns mĆ©todos diretos para resoluĆ§Ć£o de sistemas de equaƧƵes lineares intervalares.The aim of this work is to determine the solution set of some Equations of Interval Coefficients. The study use a Theory of Interval Approximation. The begining of this theory was described by [ACI91]. In this theory the equality for intervals is replaced by an approximation relation. When we make use of that relation to solve interval equations, it's possible to obtain an optimal solution, i.e., to get an interval solution that contain all of real solutions of the real equations envolved in the interval equation. By using the equality of Classical Interval Theory for solving interval equations we can not get an optimal solution, that is, the interval solution in the most of equations not consider some real solutions of real equations that belong to the interval equation. We present some basic concepts and analyse some properties at the interval space (1(R), E, -a x , 1). Different kind of functions are showed in this space in order to obtain the range, the solution caracterization and the graphic identification of the optimal and external solution region, for each kind of function. The representation of intervals in /(R) is determined in a half plane of axes X - , X+, where X - represent the lower endpoint and X+ represent the upper endpoint of the intervals. The nonregular intervals are defined in /(R), which are determined in an other half plane. In this interval space are presenting some specific concepts, as well as arithmetical operations and some remarks about nonregular intervals. The interval space (1(R), +, ā¢, C, Ex , 1) have a similar structure to a field, so it's possible to solve interval coefficients equations analogously as to solve real equations in the real space. We present the solution of linear interval equations and we determine an interval formula to solve square interval equation. We present some intervals iterated methods for functions that have degree greater than 2 that allow to get an interval solution of interval functions. Finally we show some basic concepts about the interval matrix space Af,āā(IR)) and present direct methods for the resolution of linear interval sistems
Atmospheric re-entry stability analysis of the space vehicle SARA
The aim of this paper is to present a re-entry stability analysis for the uncontrolled, non-winged, blunted cone space vehicle SARA (Atmospheric Re-entry Satellite) by taking into account a ballistic trajectory. The SARA project is a cooperation between Brazilian Space Agency (AEB) and Institute of Aeronautics and Space (IAE) to develop and construct a recoverable space vehicle to perform microgravity experiments. The Brazilian suborbital rocket VS-40 provides the insertion of the SARA capsule into microgravity environment reaching altitudes above 190 km. The analyzes presented in this work focuses on two configurations for SARA being the first, a blunted cone without aps (aero-breaking) and, the second, a blunted cone with aps. The work shows in details the re-entry stability analysis and co-simulation methodology including Newton's impact method modeling (NIM) and Computational Fluid Dynamics (CFD) software