  In recent years several research efforts focused on the development of
high-order discontinuous Galerkin (dG) methods for scale resolving simulations
of turbulent flows. Nevertheless, in the context of incompressible flow
computations, the computational expense of solving large scale equation systems
characterized by indefinite Jacobian matrices has often prevented from dealing
with industrially-relevant computations. In this work we seek to improve the
efficiency of Rosenbrock-type linearly-implicit Runge-Kutta methods by devising
robust, scalable and memory-lean solution strategies. In particular, we
introduce memory saving p-multigrid preconditioners coupling matrix-free and
matrix-based Krylov iterative smoothers. The p-multigrid preconditioner relies
on cheap block-diagonal smoother's preconditioners on the fine space to reduce
assembly costs and memory allocation, and ensures an adequate resolution of the
coarsest space of the multigrid iteration using Additive Schwarz precondioned
smoothers to obtain satisfactory convergence rates and optimal parallel
efficiency of the method. Extensive numerical validation is performed. The
Rosenbrock formulation is applied to test cases of growing complexity: the
laminar unsteady flow around a two-dimensional cylinder at Re=200 and around a
sphere at Re=300, the transitional flow problem of the ERCOFTAC T3L test case
suite with different levels of free-stream turbulence. As proof of concept, the
numerical solution of the Boeing Rudimentary Landing Gear test case at Re=10^6
is reported. A good agreement of the solutions with experimental data is
documented, as well as strong memory savings and execution time gains with
respect to state-of-the art solution strategies.
