Augmented Lagrangian / well-balanced finite volume method for compressible viscoplastic flows

Paul Vigneaux (1, 2) , Didier Bresch (3) , Enrique D. Fernandez-Nieto (4) , Ioan R. Ionescu (5)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
2 NUMED - Numerical Medicine
3 LAMA - Laboratoire de Mathématiques
4 IMUS - Departamento de Matemática Aplicada I
5 PMTM - Propriétés mécaniques et thermodynamiques des matériaux

We are interested in the simulation of shallow dense avalanches in which the snow is considered as a compressible viscoplastic fluid. Such models can be derived by taking the shallow water asymptotics of a 3D Navier-Stokes-Bingham system with free surface. From the numerical analysis point of view, such equations imply the construction of new schemes which are able to compute accurately stationary states. We here present a well-balanced finite volume/augmented Lagrangian method which couples well-balanced finite volume scheme for the spatial discretization with the augmented Lagrangian method to treat the optimization problem stem- ming from the Bingham nature of the flow equations considered here, namely a system close to the shallow water equations but with an equation on the velocity which includes the yield limit (due to the Bingham stress tensor).

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Paul Vigneaux, Didier Bresch, Enrique D. Fernandez-Nieto, Ioan R. Ionescu. Augmented Lagrangian / well-balanced finite volume method for compressible viscoplastic flows. Sixth International Conference on Computational Fluid Dynamics, ICCFD6, Jul 2010, St-Petersburg, Russia. pp.271-277. ⟨hal-00627228⟩