An agglomeration-based adaptive discontinuous Galerkin method for compressible flows

In this work, we exploit the possibility to devise discontinuous Galerkin discretizations over polytopic grids to perform grid adaptation strategies on the basis of agglomeration coarsening of a fine grid obtained via standard unstructured mesh generators. The adaptive agglomeration process is here driven by an adjoint-based error estimator. We investigate several strategies for converting the error field estimated solving the adjoint problem into an agglomeration factor field that is an indication of the number of elements of the fine grid that should be clustered together to form an agglomerated element. As a result the size of agglomerated elements is optimized for the achievement of the best accuracy for given grid size with respect to the target quantities. To demonstrate the potential of this strategy we consider problem-specific outputs of interest typical of aerodynamics, eg, the lift and drag coefficients in the context of inviscid and viscous flows test cases.