The discrete geometric conservation law and the nonlinear stability of ALE schemes for the solution of flow problems on moving grids

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Discontinuous Galerkin Solution of the Navier-Stokes Equations on Deformable Domains (2007, background): “The so-called Geometric Conservation Law (GCL), first introduced in [7], which ensures that constant flow solutions are preserved under arbitrary mesh deformations, is claimed to be a requirement to obtain schemes which are both first order spatially accurate [8] and stable in time [9].”
Fluid–structure interaction for aeroelastic applications (2004, background): “Farhat et al. [ 46 ] summarized six different time-integration schemes based on ALE formulation, some of them preserving the GCL, and showed the impact the different schemes have on solution accuracy.”
Isogeometric fluid-structure interaction: theory, algorithms, and computations (2008, background): “For a discussion of the importance of conservation and satisfaction of the DGCL for moving domain problems see [17,22,46].”
Arbitrary Lagrangian–Eulerian Methods (2004, background): “Later, Farhat et al. (2001) and other authors have studied from a theoretical viewpoint the properties of DGCL-enforcing ALE schemes.”