High order residual distribution scheme for Navier-Stokes equations.

Remi Abgrall (1, 2) , Dante de Santis (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 for the discretization of the conservation laws. In particular, emphasis is put on the construction of a third order accurate scheme. We first recall the proprieties of a Residual Distribution scheme and we show how to construct a high order scheme for advection problems, in particular for the system of the Euler equations. Furthermore, we show how to speed up the convergence of 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 scheme is tested on scalar problems and is used to discretize the Navier-Stokes equations.

Domaines: Equations aux dérivées partielles [math.AP]; Milieux fluides et réactifs

Remi Abgrall, Dante de Santis. High order residual distribution scheme for Navier-Stokes equations.. 20th AIAA Computational Fluid Dynamics Conference, AIAA, Jun 2011, Honolulu, Hawaii, United States. ⟨inria-00603625⟩