A p-adaptive Matrix-Free Discontinuous Galerkin Method for the Implicit LES of Incompressible Transitional Flows

In recent years Computational Fluid Dynamics (CFD) has become a widespread practice in industry. The growing need to simulate off-design conditions, characterized by massively separated flows, strongly promoted research on models and methods to improve the computational efficiency and to bring the practice of Scale Resolving Simulations (SRS), like the Large Eddy Simulation (LES), to an industrial level. Among the possible approaches to the SRS, an appealing choice is to perform Implicit LES (ILES) via a high-order Discontinuous Galerkin (DG) method, where the favourable numerical dissipation of the space discretization scheme plays directly the role of a subgrid-scale model. To reduce the large CPU time for ILES, implicit time integrators, that allows for larger time steps than explicit schemes, can be considered. The main drawbacks of implicit time integration in a DG framework are represented by the large memory footprint, the large CPU time for the operator assembly and the difficulty to design highly scalable preconditioners for the linear solvers. In this paper, which aims to significantly reduce the memory requirement and CPU time without spoiling the high-order accuracy of the method, we rely on a p-adaptive algorithm suited for the ILES of turbulent flows and an efficient matrix-free iterative linear solver based on a cheap p-multigrid preconditioner and a Flexible GMRES method. The performance and accuracy of the method have been assessed by considering the following test cases: (1) the T3L test case of the ERCOFTAC suite, a rounded leading edge flat plate at Re D= 3450 ; (2) the flow past a sphere at Re D= 300 ; (3) the flow past a circular cylinder at Re D= 3900.