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Numerical algorithms for the computation of steady and unsteady compressible flow over moving geometries - Application to fluid-structure interaction

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VKI PHDT 2008-01, Numerical algorithms for the computation of steady and unsteady compressible flow over moving geometries - Application to fluid-structure interaction, ISBN 978-2-930389-28-1

Numerical algorithms for the computation of steady and unsteady

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  • Numerical algorithms for the computation of steady and unsteady
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Numerical algorithms for the computation of steady and unsteady compressible flow  over moving geometries - Application to fluid-structure interaction
By Jirí Dobeš, published in 2007,   ISBN 978-2-930389-28-1
PhD Thesis from the von Karman Institute / Université Libre de Bruxelles, Belgium & Czech Technical University in Prague, Czech Republic, November 2007
Abstract

This work deals with the development of numerical methods for compressible flow simulation with application to the interaction of fluid flows and structural bodies. First, we develop numerical methods based on multidimensional upwind residual distribution (RD) schemes. Theoretical results for the stability and accuracy of the methods are given. Then, the RD schemes for unsteady problems are extended for computations on moving meshes. As a second approach, cell centered and vertex centered finite volume (FV) schemes are considered. The RD schemes are compared to FV schemes by means of the 1D modified equation and by the comparison of the numerical results for scalar problems and system of Euler equations. We present a number of two and three dimensional steady and unsteady test cases, illustrating properties of the numerical methods. The results are compared with the theoretical solution and experimental data.

In the second part, a numerical method for fluid-structure interaction problems is developed. The problem is divided into three distinct sub-problems: Computational Fluid Dynamics, Computational Solid Mechanics and the problem of fluid mesh movement. The problem of Computational Solid Mechanics is formulated as a system of partial differential equations for an anisotropic elastic continuum and solved by the finite element method. The mesh movement is determined using the pseudo-elastic continuum approach and solved again by the finite element method. The coupling of the problems is achieved by a simple sub-iterative approach. Capabilities of the methods are demonstrated on computations of 2D supersonic panel flutter and 3D transonic flutter of the AGARD 445.6 wing. In the first case, the results are compared with the theoretical solution and the numerical computations given in the references. In the second case the comparison with experimental data is presented.

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