  We develop a second-order well-balanced central-upwind scheme for the
compressible Euler equations with gravitational source term. Here, we advocate
a new paradigm based on a purely conservative reformulation of the equations
using global fluxes. The proposed scheme is capable of exactly preserving
steady-state solutions expressed in terms of a nonlocal equilibrium variable. A
crucial step in the construction of the second-order scheme is a well-balanced
piecewise linear reconstruction of equilibrium variables combined with a
well-balanced central-upwind evolution in time, which is adapted to reduce the
amount of numerical viscosity when the flow is at (near) steady-state regime.
We show the performance of our newly developed central-upwind scheme and
demonstrate importance of perfect balance between the fluxes and gravitational
forces in a series of one- and two-dimensional examples.
