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High order preserving residual distribution schemes for the laminar and turbulent Navier Stokes on arbitrary grids

Remi Abgrall 1 Dante de Santis 1
1 BACCHUS - Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5800
Abstract : This paper deals with the construction of a class of high order accurate Residual Dis- tribution schemes for the Navier Stokes equations using conformal meshes. The approx- imation of the solution is obtained using standard Lagrangian finite elements, and the total residual of the problem is constructed taking into account both the advective and the diffusive terms in order to discretize within the same scheme both parts of the gov- erning equation. To cope with the fact that the normal component of the gradients of the numerical solution is discontinuous across the faces of the elements, the gradient of the numerical solution is recovered at each degree of freedom of the grid and then interpolated with the same shape functions used for the solution. The procedure is fully described for the scalar case, and formaly extended to the system case. Linear and non-linear schemes are constructed and their accuracy is first tested with the help of manufactured solutions, and then applied to several (2D and 3D) test cases.
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https://hal.inria.fr/hal-00935547
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Remi Abgrall, Dante de Santis. High order preserving residual distribution schemes for the laminar and turbulent Navier Stokes on arbitrary grids. 21st AIAA Computational Fluid Dynamics Conference, Jul 2013, San Diego, United States. ⟨hal-00935547⟩

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