A numerical investigation on the combustion mechanics of a hybrid rocket engine is performed through unsteady Reynolds-averaged Navier-Stokes simulation. The hybrid rocket engine model is based on an experimental laboratory scale engine design operating on GOX and HDPE as a propellant. A simple convection heat flux model is used to determine the heat transfer to the fuel wall. The project is done with the goal of finding the fuel regression rate in mind, as it is an essential parameter for determining engine performance. The results show early results of the fluid- and thermodynamics occurring in the combustion chamber. Propellant mixing is shown to not be optimal as a significant part of the exit flow consists of high concentrations of oxidizer that has not reacted with the fuel. The flame temperature is shown to be relatively high inside the combustion chamber. It is concluded from the simulations that the model needs further improvement in order to accurately compute the flow as well as the heat transfer to the fuel. To determine the regression rate, radiation should be implemented into the heat transfer model.