The number density at the surface can also be calculated from a similar argument. Molecules arriving at x from x′ with speeds between c and c + dc make a contribution, dn, to the number density, n (SI unit: 1/m3), at the surface that is related to their flux at the surface, dG, by:

Following the same argument, the total incoming number density at x is given by:

The means of inverse speed (calculated using Equation 3-15) are given by:

Note that the integrand in Equation 3-20 depends only on the emitted flux, the normal, and the molecular velocity at the emitting surface (and not on the orientation or properties of the wall where the flux is arriving). Equation 3-20 can therefore be used to compute the flux arriving at any point within the flow domain, in addition to the flux arriving at surfaces. This is the basis of the number density reconstruction features and the number density calculation operator, which can be used to calculate the number density within the domain. See Number Density Reconstruction in the previous section for further details on how to use these features.

Substituting for the mean inverse velocities (using Equation 3-21 with ) the equation obtained:

where the same result holds in 2D and 3D. The outgoing number density is available in the physics interface as fmf.Nout.

This is computed in the physics interface as the dependent variable n.