Abstract (eng)
Nowadays, numerical simulations are widely used to investigate questions in physics in more detail.
Most of these questions deal with the behaviour of fluids, such as gases and liquids. A quite interesting application for this is the field of astrophysics.
Many phenomena in astrophysics are violent, for example the explosion of a star at the end of its lifetime as a supernova, where the surrounding material will be compressed. Such a compression results in a shock wave (Stoßwelle in german), which is propagating through the interstellar medium.
Since shock waves are common in many applications, it is essential that numerical simulations are able to resolve and detect them. Because different kinds of codes use different numerical methods, they have to be tested in order to be certain that their solution is a acceptable.
The "Sod Shock Tube Problem" is a method to test numerical codes, whether or not they can detect shock waves.
In this Diploma thesis the analytical and numerical solutions of the "Sod Shock Tube Problem" are compared. Therefore, first the analytical form of the continuous Euler equations is derived from major physical conservation principles.
Further on, the change from the continuous to the discrete form of the Euler equations is explained, for that purpose the finite volume method is used.
Based on this discrete description, a numerical code is written to simulate the "Sod Shock Tube Problem".
The analytical solution of the corresponding problem will be derived in dependency on the initial conditions and compared graphically with the numerical solution.
Furthermore, the dependency of the accuracy of the numerical code is investigated and discussed.