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

Abstract 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 Q 1 integration) for 3D Lagrangian compressible gas dynamics calculations. Finally we give the result of a simple convergence test in 2D.

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