  Equilibrium or stationary solutions usually proceed through the exact balance
between hyperbolic transport terms and source terms. Such equilibrium solutions
are affected by truncation errors that prevent any classical numerical scheme
from capturing the evolution of small amplitude waves of physical significance.
In order to overcome this problem, we compare two commonly adopted strategies:
going to very high order and reduce drastically the truncation errors on the
equilibrium solution, or design a specific scheme that preserves by
construction the equilibrium exactly, the so-called well-balanced approach. We
present a modern numerical implementation of these two strategies and compare
them in details, using hydrostatic but also dynamical equilibrium solutions of
several simple test cases. Finally, we apply our methodology to the simulation
of a protoplanetary disc in centrifugal equilibrium around its star and model
its interaction with an embedded planet, illustrating in a realistic
application the strength of both methods.
