An implicit p-adaptive discontinuous Galerkin solver for CAA/CFD simulations

In the last decades flow simulations have become a routine practice in many industrial fields for the aerodynamic and noise prediction. Moreover, the ever increasing interest in simulating off-design operating conditions promoted the development of high-fidelity simulation tools to overcome the modeling and accuracy limits of standard industrial codes in predicting turbulent separated flows. The discontinuous Galerkin (DG) method is well suited for this class of simulations, but today DG-based CFD and CAA (Computational AeroAcoustics) solvers cannot yet reach the computational efficiency of well-established commercial codes. As a consequence, the present paper aims at exploiting some attractive strategies, such as the adaptation of the elemental polynomial degree ((Formula presented.) -adaptation) and of the degree of exactness of quadrature rules, to enhance the computational efficiency of an implicit DG platform for CFD and CAA simulations. Moreover, a sponge layer non-reflecting boundary treatment has been also implemented for CAA. The predicting capabilities of the method have been assessed on classical CAA and CFD test cases. The proposed adaptive strategy guarantees a significant reduction ((Formula presented.)) of the computational effort for both CFD and CAA simulations, compared to uniform-order discretizations, while not spoiling the high accuracy requested to an high-fidelity simulation tool.