text: Favre averaging is the density-weighted averaging method, used in variable density or compressible turbulent flows, in place of the Reynolds averaging. The method was introduced formally by the French scientist A. J. Favre in 1965, although Osborne Reynolds has also already introduced the density-weighted averaging in 1895. The averaging results a simplistic form for the nonlinear convective terms of the Navier-Stokes equations, at the expense of making the diffusion terms complicated.