# Turbulent flows

Benjamin Krank, Niklas Fehn and Martin Kronbichler.

Numerical simulation of turbulent flows is of outstanding importance in science and engineering, since the majority of flows occurring in nature as well as in engineering such as flows in automotive and aerospace applications are turbulent.

Turbulent flow is a multiscale problem characterized by a wide range of length and time scales. Our activities are both on Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES). In a DNS, all scales from the large energy-containing scales down to the dissipative scales are resolved. For many practical flows, this will remain impractical based on computing capabilities even in the foreseeable future. In LES only the larger scales of a flow are resolved. Our research considers both explicit subgrid scale modeling where the influence of the small unresolved scales on the resolved scales is taken into account by a model and implicit LES where a stable discretization scheme, in our case based on high-order DG methods, accounts for the unresolved dissipation.

Below we present results for DNS and LES of well-known benchmark problems for transitional and turbulent incompressible flows:

### 3D Taylor-Green vortex problem at Re = 1600

The three-dimensional Taylor-Green vortex test case is a well-established benchmark problem to assess the accuracy of turbulent flow solvers and LES modeling approaches. An initially smooth velocity field containing large vortices breaks down into smaller and smaller flow structures and develops a chaotic, turbulent behavior. The above simulation has been computed with our high-order DG solver on a mesh with 128 nodes per coordinate direction using polynomial shape functions of degree 7. The above video shows iso-contours of the Q-criterion colored by the velocity magnitude. Due to the high-performance capabilities of our solver we were able to perform a DNS of the problem on a 1024^3 mesh with approximately 4e9 DoFs on SuperMUC in Garching, Germany.

### DNS of turbulent channel flow problem at Re_tau = 590

Among various benchmark flows, we have computed DNS of turbulent channel flow at Re_tau = 590 using 131 million degrees of freedom, which is visualized in the animation below.