Direct Simulation Monte-Carlo (DSMC)

Due to their low density, diluted gases should not be regarded as a continuum but as a particle system. In the DSMC method, the real gas behavior is mapped using the dynamics of a given number of simulated particles. The macroscopic quantities such as pressure, temperature, density, flow velocity, Mach number or Reynolds number are determined by a suitable averaging of the individual molecular states.

The following example simulates the cooling of argon in a closed container. A temperature below the initialized gas temperature is assigned to the vessel wall. The initialization of the molecules at t=0 is based on the Maxwell-Boltzmann distribution. The gas thus forms the state of equilibrium at a given temperature. Due to the contact of the molecules with the container wall or by intermolecular interactions the state of the molecules is changed in the course of the calculation. Looking at the velocity distributions at the beginning and end of the simulation, a Maxwell-Boltzmann distribution can be seen in both cases. The transition from one state of equilibrium to another can thus be simulated. The kinetics of the transition can also be measured by observing the temperature and pressure in the vessel. As the temperature difference between the vessel wall and the gas decreases, the instantaneous change in temperature and pressure during the simulation process becomes ever smaller. In the stationary state, these values do not change and the state of equilibrium has been reached.

In addition, the temporal thermodynamic state of the gas in the tank was investigated. The heat flow becomes correspondingly smaller due to the decreasing temperature gradient with the wall. As a result, the temperature gradient between the gas and the container walls decreases over time. The pressure can be derived from the temperature, volume and mass of argon via the ideal gas equation.