Séance Séminaire

Séminaire ACSIOM

Multiscale Godunov-type method for cell-centered discrete Lagrangian hydrodynamic

We are interested in the numerical simulation of high-speed compressible multi-materials flows. In the context of inertial confinement fusion, the sharp resolution of material interfaces is an important requirement in the design of a numerical strategy. Therefore, the Lagrangian hydrodynamic formulation is usually preferred to the Eulerian one and the main problem is to insure, at the discrete level, a consistent matching between material and kinematic velocities. For the staggered discretization, the concept of corner values is used to obtained a compatible scheme and to control artificial grid distortion. For cell-centered Lagrangian discretization, we propose an integral form of the geometrical constraint. These equations are approximated, at the limit of appropriated embedded subscales, by a subgrid Godunov-type solver. At this level the kinematic velocity associated to a vertex is linked to the surrounding material velocities by the introduction of subscale vertex pressures on each mesh interfaces. We define a compatible interpolation of these variables that insure at the mesh scale the compatibility of the discretization. The final scheme is globally conservative and the first order accurate version satisfy the entropy inequality. Some 2D and 3D applications will be presented. Related article: Multi-scale Godunov-type method for cell-centered discrete Lagrangian hydrodynamics. Maire P.-H. and Nkonga B. Journal of Computational Physics Volume 228, Issue 3, 20 February 2009 (2009) Pages 799-821.