On Well-Balanced Finite Volume Methods for Nonconservative Nonhomogeneous Hyperbolic Systems

Authors:
M. J. Castro Di´az;T. Chaco´n Rebollo;E. D. Ferna´ndez-Nieto;Carlos Pare´s
Affiliations:
-;-;-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2007

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Abstract

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.