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.
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December 1990
Research Papers
Application of an Implicit Relaxation Method Solving the Euler Equations for Time-Accurate Unsteady Problems
A. Brenneis,
A. Brenneis
Messerschmitt-Bo¨lkow-Blohm GmbH, D-8000 Mu¨nchen 80, Federal Republic of Germany
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A. Eberle
A. Eberle
Messerschmitt-Bo¨lkow-Blohm GmbH, D-8000 Mu¨nchen 80, Federal Republic of Germany
Search for other works by this author on:
A. Brenneis
Messerschmitt-Bo¨lkow-Blohm GmbH, D-8000 Mu¨nchen 80, Federal Republic of Germany
A. Eberle
Messerschmitt-Bo¨lkow-Blohm GmbH, D-8000 Mu¨nchen 80, Federal Republic of Germany
J. Fluids Eng. Dec 1990, 112(4): 510-520 (11 pages)
Published Online: December 1, 1990
Article history
Received:
May 9, 1990
Online:
May 23, 2008
Citation
Brenneis, A., and Eberle, A. (December 1, 1990). "Application of an Implicit Relaxation Method Solving the Euler Equations for Time-Accurate Unsteady Problems." ASME. J. Fluids Eng. December 1990; 112(4): 510–520. https://doi.org/10.1115/1.2909436
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