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A class of the fourth order finite volume Hermite weighted essentially non-oscillatory schemes

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Abstract

In this paper, we developed a class of the fourth order accurate finite volume Hermite weighted essentially non-oscillatory (HWENO) schemes based on the work (Computers & Fluids, 34: 642–663 (2005)) by Qiu and Shu, with Total Variation Diminishing Runge-Kutta time discretization method for the two-dimensional hyperbolic conservation laws. The key idea of HWENO is to evolve both with the solution and its derivative, which allows for using Hermite interpolation in the reconstruction phase, resulting in a more compact stencil at the expense of the additional work. The main difference between this work and the formal one is the procedure to reconstruct the derivative terms. Comparing with the original HWENO schemes of Qiu and Shu, one major advantage of new HWENO schemes is its robust in computation of problem with strong shocks. Extensive numerical experiments are performed to illustrate the capability of the method.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, 210093, China

    Jun Zhu & JianXian Qiu

  2. College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Jun Zhu

Authors
  1. Jun Zhu
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  2. JianXian Qiu
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Correspondence to JianXian Qiu.

Additional information

Corresponding author This work was partially supported by the National Natural Science Foundation of China (Grant No. 10671097), the European project ADIGMA on the development of innovative solution algorithms for aerodynamic simulations, Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry and the Natural Science Foundation of Jiangsu Province (Grant No. BK2006511)

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Zhu, J., Qiu, J. A class of the fourth order finite volume Hermite weighted essentially non-oscillatory schemes. Sci. China Ser. A-Math. 51, 1549–1560 (2008). https://doi.org/10.1007/s11425-008-0105-0

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  • DOI: https://doi.org/10.1007/s11425-008-0105-0

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