Angular Momentum preserving cell-centered Lagrangian and Eulerian schemes on arbitrary grids

Bruno Després (1) , Emmanuel Labourasse (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 DSSI - Département des Sciences de la Simulation et de l'Information

We address the conservation of angular momentum for cell-centered discretization of compressible fluid dynamics on general grids. We concentrate on the Lagrangian step which is also sufficient for Eulerian discretization using Lagrange+Remap. Starting from the conservative equation of the angular momentum, we show that a standard Riemann solver (a nodal one in our case) can easily be extended to update the new variable. This new variable allows to reconstruct all solid displacements in a cell, and is analogous to a partial Discontinuous Galerkin (DG) discretization. We detail the coupling with a second- order Muscl extension. All numerical tests show the important enhancement of accuracy for rotation problems, and the reduction of mesh imprint for implosion problems. The generalization to axi-symmetric case is detailed.

Mots clés: Compressible fluid dynamics; cell-centered Lagrangian and Eulerian schemes; general grids; angular momentum conservation; conservation laws

Domaines: Analyse numérique [math.NA]; Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Bruno Després, Emmanuel Labourasse. Angular Momentum preserving cell-centered Lagrangian and Eulerian schemes on arbitrary grids. Journal of Computational Physics, 2015, 290, pp.28-54. ⟨hal-01065105⟩