  We introduce a general framework for the construction of well-balanced finite
volume methods for hyperbolic balance laws. We use the phrase well-balancing in
a broader sense, since our proposed method can be applied to exactly follow any
solution of any system of hyperbolic balance laws in multiple spatial
dimensions and not only time independent solutions. The solution has to be
known a priori, either as an analytical expression or as discrete data. The
proposed framework modifies the standard finite volume approach such that the
well-balancing property is obtained and in case the method is high order
accurate, this is maintained under our modification. We present numerical tests
for the compressible Euler equations with and without gravity source term and
with different equations of state, and for the equations of compressible ideal
magnetohydrodynamics.
