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Abstract:

This study will present the development and results of high-order Finite Volume schemes for unstructured grids. The goal is to prepare numerical tools to perform Large Eddy Simulations with the indutrial solver elsA. These numerical schemes are based on a directional approach in order to limitate the  CPU cost and reduce the stencil. The convective part of the scheme needsto be high order and this is obtained by the use of gradients on a four-cell stencil. Two gradients are usedfor the convective part, the Green-Gauss gradient and the “UIG” gradient.  For the diffusive part, the “UIG” gradient is used. It was developped during this study and allows to recover a second-order accurate scheme. This gradient was validated  theorically and numerically on some test cases.High order numerical schemes were studied theorically with order and frequency analysis. It was shown that these schemes are fifth-order accurate on regular hexaedral elements and third order accurate on equilateral triangles. Following this analysis, these schemes were tested in 1D on an advection test case and were then validated on the convection of an isentropic vortex.

Keywords : Finite Volume, High Order convection scheme, Large Eddy Simulation, Unstructured, Directional stencil, Gradient

Jury:

Rodolphe TURPAULT         Université de Bordeaux                         Referee

Jens Dominik MUELLER    Queen Mary University of London        Referee

Nicolas GOURDAIN           ISAE Toulouse                                       Member

Hugues DENIAU                 ONERA Toulouse                                  Member

Vincent COUAILLER ONERA Châtillon                                   Member

Eric LIPPINOIS                   SNECMA                                               Industrial

Guillaume PUIGT CERFACS Toulouse                                            Advisor