At high temperatures or densities ordinary hadronic matter is expected to undergo a phase transition to a new form of matter - the quark gluon plasma. The properties of this new phase of matter as well as the transition itself is described by the theory of strong interactions - Quantum Chromo Dynamics (QCD). Although the theoretical framework thus is well known it requires large scale numerical simulations to extract quantitative information on basic thermodynamic parameters (equation of state, transition temperature) of the QCD phase diagram.
In this talk I will discuss first results from an ongoing large scale simulation that aims at an accurate determination of the transition parameters to the high temperature phase of QCD, the equation of state the transition temperature and basic properties of the phase diagram at high temperature and non-vanishing baryon number density. I will briefly comment on the application of these results in the hydrodynamic modeling of the expansion of hot and dense matter created in relativistic heavy ion collisions.