Entropy-adjoint p-adaptive discontinuous Galerkin method for the under-resolved simulation of turbulent flows

This 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 the output functional targeting areas of spurious generation of entropy. The method shows several advantages over standard output-based error estimation: 1) it is computationally inexpensive; 2) it does not require the solution of a fine-space adjoint problem; and 3) it is nonlinearly stable with respect to the primal solution for chaotic dynamic systems. In addition, the work reports on the parallel efficiency of the solver, which has been optimized through a multiconstraint domain decomposition algorithm available within the Metis 5.0 library. 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 3000; and the implicit large-eddy simulation of the flow past a circular cylinder at Re 3900 and past a square cylinder at Re 22;000. The results show a significant reduction in the number of degrees of freedom with respect to uniform order refinement with a good agreement with experimental data.