On hybrid residual distribution-Galerkin disretizations for steady and time dependent viscous laminar flows

Jiri Dobes (1) , Mario Ricchiuto (2, 3) , Remi Abgrall (4) , Herman Deconinck (5)

1 Doosan Skoda Power
2 IMB - Institut de Mathématiques de Bordeaux
3 CARDAMOM - Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts
4 UZH - Universität Zürich [Zürich] = University of Zurich
5 VKI - von Karman Institute for Fluid Dynamics

This paper is concerned with the extension of second order residual distribution (RD) schemes to time dependent viscous flows.We provide a critical analysis of the use of a hybrid RD–Galerkin approach for both steady and time dependent problems. Inparticular, as in Ricchiuto (2008) and Villedieu et al. (2011), we study the coupling of a Residual Distribution (RD) discretizationof the advection operator with a Galerkin approximation for the second order derivatives, with a Peclet dependent modulation of theupwinding introduced by the RD scheme. The final objective is to be able to achieve uniform second order of accuracy with respectto variations of the mesh size or, equivalently, of the local Peclet/Reynolds number. Starting from the scalar formulation given inthe second order case in Ricchiuto et al. (2008), we perform an accuracy and stability analysis to extend the approach to timedependentproblems, and provide thorough numerical validation of the theoretical results. The schemes, formally extended to thesystem of laminar Navier–Stokes equations, are also compared to a finite volume scheme with least-squares linear reconstructionon the solution of standard test problems. While the scalar tests show the potential of this approach in providing uniform accuracyw.r.t. the range of values of the Peclet/Reynolds number, the results for the laminar Navier–Stokes equations show that in practice,the use of Peclet number based corrections does not change dramatically the quality of the solutions obtained. This justifies thequest for new formulations.

Mots clés: Time dependent flows; Viscous flows; Hybrid scheme; Continuous Galerkin; Unstructured grids; Residual distribution

Domaines: Modélisation et simulation; Analyse numérique [math.NA]; Milieux fluides et réactifs; Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Jiri Dobes, Mario Ricchiuto, Remi Abgrall, Herman Deconinck. On hybrid residual distribution-Galerkin disretizations for steady and time dependent viscous laminar flows. Computer Methods in Applied Mechanics and Engineering, 2015, 283 (1), pp.1336-1356. ⟨10.1016/j.cma.2014.09.002⟩. ⟨hal-01087733⟩