I am working on the extension of a hybridized discontinuous Galerkin method for unsteady flow problems. It is a so-called high-order method, i.e. the error decreases with third order or more under uniform mesh refinement.

## Euler equations

Flows at high Mach numbers , i.e. supersonic flows, can be modeled by the Euler equations. These neglect viscous effects of a fluid as these only have a small influence on the resulting flow. However, in many applications these flows shocks develop. In this case we apply an artificial viscosity model for stabilizing the scheme.

Close-up of the shock interactions of a double Mach wedge.

## Navier-Stokes equations

For modeling viscous flow we use the compressible Navier-Stokes equations. These flows develop boundary layers when the fluid passes rigid walls since no-slip condition conditions are enforced on these surfaces.

A `classical' phenomenon for viscous flows is the Karman vortex street. If a viscous fluid flows around an obstacle at moderate Reynolds numbers vortices shed periodically. It has been intensively studied by many scientists. Therefore, it is often used for verification of numerial methods. The actual behavior of the flow depends on the Reynolds number and the shape of the obstacle.

You can also let the fluid flow around obstacles such as the CMAT writing (see also top left of the homepage):

More images will follow soon!

## References

Please look in our papers and especially the references therein.