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Construction of a high order Residual Distribution scheme for complex viscous flows

Remi Abgrall 1, 2 Dante de Santis 1 Mario Ricchiuto 1, 2 
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 : In this work we describe the use of the Residual Distribution schemes applied to the discretization of conservation laws. In particular, emphasis is put on the construction of a third order accurate scheme. We first recall the properties of a Residual Distribution scheme and we show how to construct a high order scheme for advection problems. Furthermore, we show how to speed up the convergence of the implicit scheme to the steady solution by the means of the Jacobian-free technique. We then extend the scheme to the case of advection-diffusion problems. In particular, we propose a new approach in which the residuals of the advection and diffusion terms are distributed together to get high order accuracy. Due to the continuous approximation of the solution, the gradients of the variables are reconstructed at the nodes and then interpolated on the elements. The numerical scheme is used to discretize the advection-diffusion scalar problem and the compressible Navier-Stokes equations.
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Submitted on : Tuesday, July 10, 2012 - 11:55:11 PM
Last modification on : Thursday, January 20, 2022 - 5:31:40 PM
Long-term archiving on: : Thursday, December 15, 2016 - 10:17:02 PM


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  • HAL Id : hal-00716621, version 1



Remi Abgrall, Dante de Santis, Mario Ricchiuto. Construction of a high order Residual Distribution scheme for complex viscous flows. Seventh International Conference on Computational Fluid Dynamics (ICCFD7), Jul 2012, Big Island, Hawaii,, United States. ⟨hal-00716621⟩



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