High-Order discontinuous Galerkin methods for incompressible flows

The spatial discretization of the unsteady incompressible Navier-Stokes equations is stated as a system of Differential Algebraic Equations (DAEs), corresponding to the conservation of momentum equation plus the constraint due to the incompressibility condition. Runge-Kutta methods applied to the solution of the resulting index-2 DAE system are analyzed, allowing a critical comparison in terms of accuracy of semi-implicit and fully implicit Runge-Kutta methods. Numerical examples, considering a discontinuous Galerkin Interior Penalty Method with piecewise solenoidal approximations, demonstrate the applicability of the approach, and compare its performance with classical methods for incompressible flows.