  We present a new well-balanced finite volume method within the framework of
the finite volume evolution Galerkin (FVEG) schemes. The methodology will be
illustrated for the shallow water equations with source terms modelling the
bottom topography and Coriolis forces. Results can be generalized to more
complex systems of balance laws. The FVEG methods couple a finite volume
formulation with approximate evolution operators. The latter are constructed
using the bicharacteristics of multidimensional hyperbolic systems, such that
all of the infinitely many directions of wave propagation are taken into
account explicitly. We derive a well- balanced approximation of the integral
equations and prove that the FVEG scheme is well-balanced for the stationary
steady states as well as for the steady jets in the rotational frame. Several
numerical experiments for stationary and quasi-stationary states as well as for
steady jets confirm the reliability of the well-balanced FVEG scheme.
