Abstract:
We consider numerical schemes for 2 2 hyperbolic conservation laws on
graphs. The hyperbolic equations are given on the spatially one{dimensional arcs and
are coupled at a single point, the node, by a nonlinear coupling condition. We develop
high-order nite volume discretizations for the coupled problem. The reconstruction
of the
uxes at the node is obtained using derivatives of the parameterized algebraic
conditions imposed at the nodal points in the network. Numerical results illustrate
the expected theoretical behavior.
