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Multi-Dimentional Upwind Schemes for the Euler Equations on Unstructured Grids
Mounir Aksas, Abdelmouman H. Benmachiche
Pages - 185 - 200     |    Revised - 05-05-2009     |    Published - 18-05-2009
Volume - 3   Issue - 2    |    Publication Date - April 2009  Table of Contents
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KEYWORDS
CFD, Euler equation, Unstructured triangular meshes, Upwind, Fluctuation, Roe
ABSTRACT
In the last few years, upwind methods have become very popular in the modeling of advection dominated flows and in particular those which contain strong discontinuities. For more than a decade, these methods have been used successfully to solve numerically the one-dimensional Euler equations [10]. Fluctuation distribution has been recently [3] introduced as an alternative to conventional upwinding. In contrast to standard upwinding the fluctuation distribution approach extends naturally to multidimensional flow without requiring any splitting along coordinate directions. The technique uses a narrow-stencil, local, piecewise linear reconstruction of the flow field solution. The flow field is updated in time by propagating a subset of eigenmodes of the convective operator. Different choices of the eigenmode subset lead to different fluctuation distribution schemes [8]. In this paper the presented models of fluctuation distribution for the Euler equations have reached the stage where they can be used reliably to achieve maximal computational efficiency to practical steady state problems in aerodynamics (Supersonic oblique shock reflection, Flow in a channel with a Bump, Symmetric Constricted channel flows, flow around NACA 0012 aerofoil, flows in a turbine-blade cascade VKI LS-59 ).
CITED BY (1)  
1 Casoni, E., Peraire, J., & Huerta, A. (2012). Un método de captura de choques basado en las funciones de forma para Galerkin discontinuo de alto orden. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, 28(4), 204-213.
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Dr. Mounir Aksas
- Algeria
m_aksas@hotmail.com
Mr. Abdelmouman H. Benmachiche
- Algeria