High order preserving residual distribution schemes for advection-diffusion scalar problems on arbitrary grids
type: Dataset
description: 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 we consider range from pure difusion 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 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. Linear and non-linear schemes are constructed and their accuracy is tested with the discretization of advection-diffusion and anisotropic diffusion problems.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 we consider range from pure difusion 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 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. Linear and non-linear schemes are constructed and their accuracy is tested with the discretization of advection-diffusion and anisotropic diffusion problems.
identifier: Report N°: RR-8157
issued: 2026-06-02T05:06:28.095610
language: en
modified: 2026-06-02T05:06:28.095625
contact point: Organization
  fn: CCSD
keyword: acm-g-mathematics-of-computingg1-numerical-analysis
keyword: acm-i-computing-methodologiesi6-simulation-and-modeling
keyword: advection-diffusion-problems
keyword: gradient-recovery
keyword: higher-order-schemes
keyword: infoeu-reposemanticsreport
keyword: mathmath-namathematics-mathnumerical-analysis-mathna
keyword: reports
keyword: residual-distribution
keyword: spifluidengineering-sciences-physicsreactive-fluid-environment
keyword: viscous-term
landing page: https://inria.hal.science/hal-00758930

High order preserving residual distribution schemes for advection-diffusion scalar problems on arbitrary grids
type: Distribution
format: HTML
issued: 2026-06-02T05:06:28.126411
modified: 2026-06-02T05:06:28.041496
access URL: https://inria.hal.science/hal-00758930

test_moissonnage_selune
type: Agent