A second-order time-accurate ALE Lagrange–Galerkin method applied to wind engineering and control of bridge profiles Original Research Article

In this paper, we propose a second-order time-accurate ALE formulation of Lagrange–Galerkin methods for the transient solution of Navier–Stokes equations for an incompressible fluid in a moving domain. Following a previous work [Rev. Européenne Élém. Finis 8 (1999) 659], we show that this time discretization, based on a backward differentiation formula and the construction of characteristic paths in a grid-relative velocity field, leads to second-order time-accuracy. Numerical results are compared with those given by a first-order approach. The numerical diffusion is dramatically reduced, which makes the use of turbulence model quasi-mandatory for realistic wind engineering applications. The software developed was also used to solve elementary control problems. The solution method is based on the linearization of the discretized problem (including the method of characteristics). The formulation and implementation were successfully completed and will be detailed elsewhere.