The hydrodynamical description for a discrete velocity model of gas. (English) Zbl 0652.76053
For a model of gas composed of identical particles with velocities restricted to a given finite set of vectors, the Boltzmann equation is replaced by a system of nonlinear coupled differential equations. The Chapman-Enskog method can be applied, and it gives the Navier-Stokes equations associated to the model. For the general model, we show that the dissipative terms in the Navier-Stokes equations do not depend on the mean number density nor on its gradient. For a gas near a homogeneous state, we give the transport coefficients explicitly.
MSC:
76P05 | Rarefied gas flows, Boltzmann equation in fluid mechanics |
76N15 | Gas dynamics (general theory) |
82B40 | Kinetic theory of gases in equilibrium statistical mechanics |
82D15 | Statistical mechanics of liquids |