Design and analysis of ALE schemes with provable second-order time-accuracy for inviscid and viscous flow simulations

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Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity (2006, methodology): “case, two finite difference Newton–Krylov iterations are performed at each time-step to solve the algebraic system of nonlinear fluid equations [24].”
A moving mesh finite volume interface tracking method for surface tension dominated interfacial fluid flow (2012, background): “Farhat and Geuzaine [22,21] showed that satisfaction of the DGCL is a necessary condition for any temporal discretisation scheme to preserve on moving grids the non-linear stability properties of its fixed-grid counterpart but they also showed that satisfaction of the DGCL is not a sufficient condit”
Adjoint-Based Sensitivity Formulation for Fully Coupled Unsteady Aeroelasticity Problems (2009, methodology): “(7) results in the mathematical description of the GCL, as stated next [18,19]:”