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High-Order Preserving Residual Distribution Schemes for Advection-Diffusion scalar problems on arbitrary grids

Remi Abgrall 1 Dante Desantis 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 : This paper deals with the construction of a class of high-order accurate residual distribution schemes for advection-diffusion problems using conformal meshes. The problems considered range from pure diffusion to pure advection. The approximation 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 with the same scheme both parts of the governing equation. To cope with the fact that the normal component of the gradient of the numerical solution is discontinuous across the faces of the elements, the gradient of the numerical solution is reconstructed at each degree of freedom of the grid and then interpolated with the same shape functions used for the solution. Linear and nonlinear schemes are constructed and their accuracy is tested with the discretization of advection-diffusion and anisotropic diffusion problems.
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https://hal.inria.fr/hal-01087924
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Submitted on : Thursday, November 27, 2014 - 9:51:41 AM
Last modification on : Friday, March 4, 2022 - 4:29:15 PM

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Remi Abgrall, Dante Desantis, Mario Ricchiuto. High-Order Preserving Residual Distribution Schemes for Advection-Diffusion scalar problems on arbitrary grids. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2014, 36 (3), pp.A955-A983. ⟨10.1137/12090143X⟩. ⟨hal-01087924⟩

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