This bachelor thesis deals with the simulation of smoke in a particle system. Here the possibilities are investigated to implement smoke as realistically as possible in a particle system and to calculate it in real time. The physical simulation is based on the work of Müller and Ren, who deal with the physical properties of fluids and gases. The simulation was implemented on the GPU using C++, OpenGL and the compute shaders available in OpenGL. Special attention was paid to the performance of the simulation. Hoetzlein techniques are used to accelerate the particle system. Two acceleration methods were then implemented and compared. The runtime, but also the used memory space of the GPU is discussed.