title: A Well-Balanced Path-Integral f-Wave Method for Hyperbolic Problems with Source Terms.
abstract: Systems of hyperbolic partial differential equations with source terms (balance laws) arise in many applications where it is important to compute accurate time-dependent solutions modeling small perturbations of equilibrium solutions in which the source terms balance the hyperbolic part. The f-wave version of the wave-propagation algorithm is one approach, but requires the use of a particular averaged value of the source terms at each cell interface in order to be "well balanced" and exactly maintain steady states. A general approach to choosing this average is developed using the theory of path conservative methods. A scalar advection equation with a decay or growth term is introduced as a model problem for numerical experiments.
authors.affiliation: Department of Applied Mathematics, University of Washington, Box 352420, Seattle, WA 98195-2420, USA.
authors.forename: Randall J
authors.initials: RJ
authors.lastname: Leveque
keywords: Hyperbolic partial differential equations; Source terms; Well-balanced methods