For high Knudsen numbers [0] the Navier-Stokes equations will be inaccurate. You can use a different approach based on the Boltzmann equation [1] like DSMC [2]

For high Knudsen numbers [0] the Navier-Stokes equations will be inaccurate. You can use a different approach based on the Boltzmann equation [1] like DSMC [2] for example. As I wrote elsewhere there are good reasons to not use the Boltzmann equation everywhere [3]. Navier-Stokes is simpler and often completely adequate. There are surely other situations as well; this is just what comes immediately to mind as I had a class covering some of this. [0] https://en.wikipedia.org/wiki/Knudsen_number https://en.wikipedia.org/wiki/Knudsen_number [1] https://en.wikipedia.org/wiki/Boltzmann_equation https://en.wikipedia.org/wiki/Boltzmann_equation [2] https://en.wikipedia.org/wiki/Direct_simulation_Monte_Carlo https://en.wikipedia.org/wiki/Direct_simulation_Monte_Carlo [3] https://news.ycombinator.com/item?id=31054992 https://news.ycombinator.com/item?id=31054992