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
2 IMB - Institut de Mathématiques de Bordeaux

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.

Mots clés: Navier-Stokes equations; High order schemes; Residual distribution; Computational Fluid Dynamics

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

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⟩