Direct simulation Monte Carlo (DSMC)

The Direct Simulation Monte Carlo method[1] is used to simulate gases with low density – or to be precise: If the mean free path of the gas particles/molecules is large compared to a typical physical length of the system (high Knudsen number) the Navier-Stokes equations are no longer valid and DSMC is needed.

The idea is to simulate the movement and collisions of the particles directly, but each simulated particle represents several real particles (~10³). Some further assumptions are made:

Cells

The cells are composed of smaller elements that form a regular grid. An element is part of a cell if the center of the cell is closer to that element than any other.

Boundaries

Particles enter the simulation from the x=0 surface and leave at x>xMax. Every other surface reflects the particles.

Additional boundaries can be given by functions x(y,z), y(z,x) and z(x,y). Reflections are calculated by (1) interpolating of these functions lineary to get the position of the impact, (2) calculating a numerical derivative at that position to get a normal of the surface and (3) changing the direction of the velocity of the particle.

Limitations/problems of this implementation


[1] The DSMC method, GA Bird, CreateSpace Independent Publishing Platform, 2013