Séminaire AA — Variational Cell-Centered Direct ALE Scheme for Compressible Flows: Consistency and Structure Preservation in the Lagrangian Limit
Date(s) : 24/03/2026 iCal
11h00 - 12h00
The numerical simulation of compressible flows on moving meshes poses significant challenges due to the need to simultaneously preserve conservation laws, geometric consistency,
and thermodynamic structure under strong deformation and complex flow regimes. Arbitrary Lagrangian–Eulerian (ALE) methods [1] provide a flexible framework to address these
challenges, but maintaining robustness and physical fidelity across the full spectrum from
Eulerian to Lagrangian descriptions remains difficult.
In this work, we present a variational, cell-centered ALE formulation based on the Ge-
ometry, Energy, and Entropy Compatible (GEEC) framework [3]. In this approach, the
discretization is performed at the level of the underlying fluid Lagrangian, and the dis-
crete evolution equations are obtained through a least-action principle. This construction
naturally enforces key structural properties, including exact conservation of mass, momentum, and total energy, as well as geometric compatibility between mesh motion and control
volumes and entropy consistency in the absence of physical dissipation.
Within this framework, particular attention is given to the interplay between mass trans-
port and pressure forces, which are intrinsically coupled through the variational structure.
We discuss the behavior of the scheme in regimes approaching the Lagrangian limit, where
standard discretizations may exhibit loss of symmetry and degraded conservation proper-
ties. A formulation is presented that maintains consistent pressure coupling and geometric
conservation under mesh motion, ensuring stable and physically meaningful behavior even
in strongly deforming configurations [2].
The resulting method provides a robust and structure-preserving approach for compressible flow simulation on arbitrarily moving meshes. Its performance is illustrated on
representative test cases involving shocks and highly compressive regimes. The first results
of these extensions to multi-material and multiphase flows will also be demonstrated.
References
[1] C. W. Hirt, A. A. Amsden, and J. L. Cook. An arbitrary Lagrangian–Eulerian computing
method for all flow speeds. J. Comput. Phys., 14(3):227–253, 1974.
[2] Ksenia Kozhanova, Gabriel Farag, Antoine Llor, Pierre Boivin, et al. Variational cell-
centered ale scheme for compressible flows: Improved consistency in the lagrangian limit.
Computers and Fluids, 2025. Preprint.
[3] T. Vazquez-Gonzalez, A. Llor, and C. Fochesato. A novel GEEC (Geometry, Energy, and
Entropy Compatible) procedure applied to a staggered direct-ALE scheme for hydrodynamics. Eur. J. Mech. B Fluids, 65:494–514, 2017.
Emplacement
I2M Saint-Charles - Salle de séminaire
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