Journal
of Scientific Computing 48(2010), pp. 209-226.
Special issue for the proceedings of
NumHyp2009,
a workshop on Numerical approximations of hyperbolic
systems with source terms and applications, Castro-Urdiales, Spain, 2009
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.
Preprint: wbfwave10.pdf
Simulations and code to accompany this paper: See the Instructions at the bottom of this README file to obtain the version of Clawpack 4.4 used for these tests.
Tar file of code: wbfwave10.tar.gz