On well-balanced finite volume methods for nonconservative nonhomogeneous hyperbolic systems

In this work we introduce a general family of finite volume methods for nonhomogeneous hyperbolic systems with nonconservative terms. We prove that all of them are "asymptotically well-balanced": they preserve all smooth stationary solutions in all the domain except for a set whose measure tends to zero as Delta x tends to zero. This theory is applied to solve the bilayer shallow-water equations with arbitrary cross-section. Finally, some numerical tests are presented for simplified but meaningful geometries, comparing the computed solution with approximated asymptotic analytical solutions.