Improved p-Multigrid Approach for the Discontinuous Galerkin Solution of Turbulent Flows

Finite Element Methods are increasingly used in various scientific and industrial applications due to their advantageous combination of high-order accuracy, geometric flexibility, and robustness. However, their computational cost increases rapidly when the solution is discretised with higher-order polynomial approximations. For this reason, much research has been devoted to overcome this drawback. This work presents the implementation of an improved p-MultiGrid algorithm based on the nonlinear Full Approximation Scheme in a discontinuous Galerkin solver for the solution of the three-dimensional and compressible Navier-Stokes and Reynolds-Average Navier-Stokes equations for flows in both laminar and turbulent conditions. Only the application of these algorithms, in both the h and p forms, to the solution of the Euler and Navier-Stokes equations for laminar flows is well documented in the literature.