  Metriplectic dynamics is applied to compute equilibria of fluid dynamical
systems. The result is a relaxation method in which Hamiltonian dynamics
(symplectic structure) is combined with dissipative mechanisms (metric
structure) that relaxes the system to the desired equilibrium point. The
specific metric operator, which is considered in this work, is formally
analogous to the Landau collision operator. These ideas are illustrated by
means of case studies. The considered physical models are the Euler equations
in vorticity form, the Grad-Shafranov equation, and force-free MHD equilibria.
