High-order arbitrary Lagrangian–Eulerian discontinuous Galerkin methods for the incompressible Navier–Stokes equations

This paper presents robust discontinuous Galerkin methods for the incompressible Navier-Stokes equations on moving meshes. High-order accurate arbitrary Lagrangian-Eulerian formulations are proposed in a unified framework both monolithic as well projection or splitting-type solvers. The is flexible, allows implicit and explicit of convective term, adaptive time-stepping. with ALE transport term solved deformed geometry storing one instance mesh that updated from time step to next. Discretization space applied discrete so all weak forms mass matrices evaluated at end current step. design ensures fulfill geometric conservation law automatically, shown theoretically demonstrated numerically by example free-stream preservation test. We discuss peculiarities related imposition boundary conditions intermediate steps projection-type ingredients needed preserve high-order accuracy. show this work maintain formal order accuracy Moreover, we demonstrate robustness under-resolved turbulent flows.