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

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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.

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  1. Department of Applied Mathematics, University of Washington, Box 352420, Seattle, WA, 98195-2420, USA

    Randall J. LeVeque

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  1. Randall J. LeVeque
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LeVeque, R.J. A Well-Balanced Path-Integral f-Wave Method for Hyperbolic Problems with Source Terms. J Sci Comput 48, 209–226 (2011). https://doi.org/10.1007/s10915-010-9411-0

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  • DOI: https://doi.org/10.1007/s10915-010-9411-0

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