Weak consistency of the cell-centered Lagrangian GLACE scheme on general meshes in any dimension

We study the consistency in the weak sense of the cell-centered Lagrangian scheme GLACE. The main result is that GLACE is weakly consistent on general meshes in any dimension. The proof relies on a new formula for some geometric vectors defined at the corners of the cell, and which are basic Lagrangian objects. It validates theoretically the use of isoparametric elements (based on Q1 integration) for 3D Lagrangian compressible gas dynamics calculations. Finally we give the result of a simple convergence test in 2D.