We consider a scalar partial differential equation of hyperbolic type in conservation form on a network composed by n incoming and m outgoing arcs, connected together at a node. We deal with the Riemann problem at the node and we present various Riemann solvers, introduced in the literature, satisfying some general properties, which ensure existence of a solution to a Cauchy problem.
Garavello, M., Piccoli, B. (2009). Riemann solvers for conservation laws at a node. In Hyperbolic problems: theory, numerics and applications, part 2 (pp.595-604). AMS.
Riemann solvers for conservation laws at a node
GARAVELLO, MAURO;
2009
Abstract
We consider a scalar partial differential equation of hyperbolic type in conservation form on a network composed by n incoming and m outgoing arcs, connected together at a node. We deal with the Riemann problem at the node and we present various Riemann solvers, introduced in the literature, satisfying some general properties, which ensure existence of a solution to a Cauchy problem.
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