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High-Order Well-Balanced Finite Difference WENO Schemes for a Class of Hyperbolic Systems with Source Terms

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Abstract

In this paper, we generalize the high order well-balanced finite difference weighted essentially non-oscillatory (WENO) scheme, designed earlier by us in Xing and Shu (2005, J. Comput. phys. 208, 206–227) for the shallow water equations, to solve a wider class of hyperbolic systems with separable source terms including the elastic wave equation, the hyperbolic model for a chemosensitive movement, the nozzle flow and a two phase flow model. Properties of the scheme for the shallow water equations (Xing and Shu 2005, J. Comput. phys. 208, 206–227), such as the exact preservation of the balance laws for certain steady state solutions, the non-oscillatory property for general solutions with discontinuities, and the genuine high order accuracy in smooth regions, are maintained for the scheme when applied to this general class of hyperbolic systems

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Authors and Affiliations

  1. Department of Mathematics, Brown University, Providence, RI, 02912, USA

    Yulong Xing

  2. Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA

    Chi-Wang Shu

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  1. Yulong Xing
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  2. Chi-Wang Shu
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Correspondence to Yulong Xing.

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Xing, Y., Shu, CW. High-Order Well-Balanced Finite Difference WENO Schemes for a Class of Hyperbolic Systems with Source Terms. J Sci Comput 27, 477–494 (2006). https://doi.org/10.1007/s10915-005-9027-y

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  • DOI: https://doi.org/10.1007/s10915-005-9027-y

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