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

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