Space-time discontinuous Galerkin method for compressible flow

Flows are common phenomena in our daily live which explains the prominent part fluid dynamics has been playing in the scientific endeavor over the past centuries. The behavior of Newtonian fluids is presently well understood and expressed in a complete set of physical models based on the principle of conservation. This principle states that mass, momentum and energy are conserved, but its simplicity belies the diversity and complexity found in fluid dynamics.
The model of interest in this thesis describes compressible flow with viscous effects and is mathematically formulated by the Navier-Stokes equations. Compressibility is considered a property of the flow: air may be modeled as incompressible at moderate flow speed since compressibility effects such as shocks only occur as the speed approaches the speed of sound. Viscous effects are important near solid surfaces where the fluid adheres to the object, influencing lift and drag. The model is valid for many applications in aerodynamics, however, exact solutions of the equations can only be found in the simplest of cases.
During the past decades, emphasis has shifted from experiments and analytical techniques to the numerical solution of the model equations, made possible by the development of micro-processors. Numerical simulations effectively complement wind tunnel experiments, which are essential in designing aircraft but have their own limitations. The standing shock on the wing of an aircraft in transonic flight, for example, may reflect on the walls of the wind tunnel and disturb the measurements.