Discontinuity-capturing directional dissipation (DCDD) in computation of turbulent flows

Stabilized formulations are now widely used in the computation of turbulent flows. The Streamline-Upwind/Petrov-Galerkin (SUPG) and Pressure-Stabilizing/ Petrov-Galerkin (PSPG) methods are among the most popular stabilized formulations. The Discontinuity Capturing Directional Dissipation (DCDD) was first introduced as a complement to the SUPG and PSPG stabilizations for the computation of incompressible flows in the presence of sharp solution gradients. The DCDD stabilization takes effect where there is a sharp gradient in the velocity field and introduces dissipation in the direction of that gradient. The length scale used in defining the DCDD stabilization is based on the solution gradient. Here we describe how the DCDD stabilization, in combination with the SUPG and PSPG stabilizations, can be applied to computation of turbulent flows. We examine the similarity between the DCDD stabilization and a purely dissipative energy cascade model. To evaluate the performance of the DCDD stabilization, we compute as test problems a plane channel flow and an axial flow fan rotor.