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RESEARCH PAPERS

Application of an Implicit Relaxation Method Solving the Euler Equations for Time-Accurate Unsteady Problems

[+] Author and Article Information
A. Brenneis, A. Eberle

Messerschmitt-Bölkow-Blohm GmbH, D-8000 München 80, Federal Republic of Germany

J. Fluids Eng 112(4), 510-520 (Dec 01, 1990) (11 pages) doi:10.1115/1.2909436 History: Received May 09, 1990; Online May 23, 2008

Abstract

A numerical procedure is presented for computing time-accurate solutions of flows about two and three-dimensional configurations using the Euler equations in conservative form. A nonlinear Newton method is applied to solve the unfactored implicit equations. Relaxation is performed with a point Gauss-Seidel algorithm ensuring a high degree of vectorization by employing the so-called checkerboard scheme. The fundamental feature of the Euler solver is a characteristic variable splitting scheme (Godunov-type averaging procedure, linear locally one-dimensional Riemann solver) based on an eigenvalue analysis for the calculation of the fluxes. The true Jacobians of the fluxes on the right-hand side are used on the left-hand side of the first order in time-discretized Euler equations. A simple matrix conditioning needing only few operations is employed to evade singular behavior of the coefficient matrix. Numerical results are presented for transonic flows about harmonically pitching airfoils and wings. Comparisons with experiments show good agreement except in regions where viscous effects are evident.

Copyright © 1990 by The American Society of Mechanical Engineers
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