An entropy-adjoint p-adaptive discontinuous galerkin method for the under-resolved simulation of turbulent flows

The paper presents an approach to mesh adaptation suitable for scale resolving simulations. The methodology is based on the entropy adjoint approach, which corresponds to a standard output-based adjoint method with output functional targeting areas of spurious generation of entropy. The method shows several advantages over standard output-based error estimation: i) it is computationally inexpensive, ii) does not require the solution of a fine-space adjoint problem, and iii) is nonlinearly stable with respect to the primal solution for chaotic dynamical systems. In addition, the work reports on the parallel efficiency of the solver, which has been optimized through a multi-constraint domain decomposition algorithm available within the Metis 5.0 library.1 The reliability, accuracy, and efficiency of the approach are assessed by computing three test cases: the two-dimensional, laminar, chaotic flow around a square at Re = 3 000, the implicit Large Eddy Simulation (LES) of a circular cylinder at Re = 3 900, and the ILES of a square cylinder at Re = 22 000. The results show significant reduction in the number of DoFs with respect to uniform order-refinement, and good agreement with experimental data.