**A Well-Balanced Path-Integral f-wave Method for
Hyperbolic Problems with Source Terms
**

by Randall J. LeVeque,

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

DOI: 10.1007/s10915-010-9411-0

**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