Output-based mesh adaptation for high order Navier-Stokes simulations on deformable domains

We present an output-based mesh adaptation strategy for Navier-Stokes simulations on deforming domains. The equations are solved with an arbitrary Lagrangian-Eulerian (ALE) approach, using a discontinuous Galerkin finite-element discretization in both space and time. Discrete unsteady adjoint solutions, derived for both the state and the geometric conservation law, provide output error estimates and drive adaptation of the space-time mesh. Spatial adaptation consists of dynamic order increment or decrement on a fixed tessellation of the domain, while a combination of coarsening and refinement is used to provide an efficient time step distribution. Results from compressible Navier-Stokes simulations in both two and three dimensions demonstrate the accuracy and efficiency of the proposed approach. In particular, the method is shown to outperform other common adaptation strategies, which, while sometimes adequate for static problems, struggle in the presence of mesh motion. We present output-based mesh adaptation for Navier-Stokes on deforming domains.Space-time adaptation is driven by unsteady state and GCL adjoints.Significant reductions in mesh size and CPU time are obtained in 2 and 3 dimensions.If the GCL is used, a GCL adjoint is necessary for accurate error estimates.However, accurate outputs can often be obtained without the GCL.

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