We present a new cell-centered multi-material Arbitrary Lagrangian Eulerian (ALE) scheme to solve the compressible gaz dynamics equations on two-dimensional unstructured grid. Our ALE method is of the explicit time-marching Lagrange plus remap type. Namely, it involves the following three phases: a Lagrangian phase wherein the flow is advanced using a cell-centered scheme; a rezone phase in which the nodes of the computational grid are moved to more optimal positions; a cellcentered remap phase which consists in interpolating conservatively the Lagrangian solution onto the rezoned grid. The multi-material modeling utilizes either concentration equations for miscible fluids or the Volume Of Fluid (VOF) capability with interface reconstruction for immiscible fluids. The main original feature of this ALE scheme lies in the introduction of a new mesh relaxation procedure which keeps the rezoned grid as close as possible to the Lagrangian one. In this formalism, the rezoned grid is defined as a convex combination between the Lagrangian grid and the grid resulting from condition number smoothing. This convex combination is constructed through the use of a scalar parameter which is a scalar function of the invariants of the Cauchy-Green tensor over the Lagrangian phase. Regarding the cell-centered remap phase, we employ two classical methods based on a partition of the rezoned cell in terms of its overlap with the Lagrangian cells. The first one is a simplified swept face-based method whereas the second one is a cell-intersection-based method. Our multi-material ALE methodology is assessed through several demanding two-dimensional tests. The corresponding numerical results provide a clear evidence of the robustness and the accuracy of this new scheme.

Two main paths are now under investigation that aim at thermonuclear ignition of hydrogen isotopes using lasers: central hot spot self-ignition and externally driven fast ignition of preassembled fuel. A third, intermediate, scheme is shock ignition, which combines the simplicity of self-ignition capsules to the hydrodynamic robustness of the fast ignition fuel assembly. This study addresses the potential of shock ignition for the HiPER project and provides a preliminary assessment of possible detrimental effects. Monodimensional simulations are performed to study the robustness of the ignition scheme in terms of shock launching time and laser power. Bidimensional simulations address the sensitivity of shock ignition to irradiation nonuniformity and to low mode asymmetries of the fuel assembly.

We present a new reconnection-based Arbitrary Lagrangian Eulerian (ALE) method. The main elements in a standard ALE simulation are an explicit Lagrangian phase in which the solution and grid are updated, a rezoning phase in which a new grid is defined, and a remapping phase in which the Lagrangian solution is transferred (conservatively interpolated) onto the new grid. In standard ALE methods the new mesh from the rezone phase is obtained by moving grid nodes without changing connectivity of the mesh. Such rezone strategy has its limitation due to the fixed topology of the mesh. In our new method we allow connectivity of the mesh to change in rezone phase, which leads to general polygonal mesh and allows to follow Lagrangian features of the mesh much better than for standard ALE methods. Rezone strategy with reconnection is based on using Voronoi tessellation. We demonstrate performance of our new method on series of numerical examples and show it superiority in comparison with standard ALE methods without reconnection.