On the essential role of kinetic theory in numerical methods for fluid-dynamic equations

The essential role of kinetic theory in the numerical methods for the Navier‐Stokes equations (compressible and incompressible) is discussed. The easy theory of characteristics for kinetic equations brings about drastic simplification of approximate Riemann solver employed in various shock‐capturing schemes. The lattice Boltzmann method is shown to essentially solve an artificial compressibility PDE system. The asymptotic behavior of solution of kinetic equations for small mean free path does not play the essential role in these kinetic numerical methods.