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High order discretisation by Residual Distribution schemes

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VKI PHDT 2010-05, Nadège Villedieu, Université Libre de Bruxelles, Belgium, November 2009, ISBN 978-2-87516-004-1

High order discretisation by Residual Distribution schemes

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High order discretisation by Residual Distribution schemes

Nadège Villedieu

VKI PHDT 2010-05, Université Libre de Bruxelles, Belgium, November 2009, ISBN 978-2-87516-004-1

This project is concerned with the development of third and fourth order residual distribution schemes for compressible flow with shocks. Indeed, it is now widely recognized that very higher order schemes offer a potential of higher efficiency and are even critical for certain applications like aero-acoustics, but also for LES and DNS. In this optics the goal of this Phd is to construct monotone third and fourth order residual distributive
schemes and to apply them in aero-acoustics problems for sound propagation using the linearized Euler equations.

The method starts from a finite element approximation on Lagrangian elements of arbitrary order defined on triangular elements (P1, P2, P3 …). It uses a sub-triangulation of the higher order element to distribute in a
nonlinear way the higher order residual computed on the sub-triangle, towards the nodes of the sub-triangle. Over the last year the improvement of the shock detection and the high order descretization of source terms have been developed.

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