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Fifth-Order Hermite Targeted Essentially Non-oscillatory Schemes for Hyperbolic Conservation Laws

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Abstract

We present a targeted essentially non-oscillatory (TENO) scheme based on Hermite polynomials for solving hyperbolic conservation laws. Hermite polynomials have already been adopted in weighted essentially non-oscillatory (WENO) schemes (Qiu and Shu in J Comput Phys 193:115–135, 2003). The Hermite TENO reconstruction offers major advantages over the earlier reconstruction; namely, it is a compact Hermite-type reconstruction and has low dissipation by virtue of TENO’s stencil voting strategy. Next, we formulate a new high-order global reference smoothness indicator for the proposed scheme. The flux calculations and time-advancing schemes are carried out by the local Lax–Friedrichs flux and third-order strong-stability-preserving Runge–Kutta methods, respectively. The scalar and system of the hyperbolic conservation laws are demonstrated in numerical tests. In these tests, the proposed scheme improves the shock-capturing performance and inherits the good small-scale resolution of the TENO scheme.

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Data Availability

The data are available from the corresponding author on reasonable request.

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Acknowledgements

The first author wishes to thank Dr. Xiaofeng Cai, who provided essential support for this work. The authors gratefully acknowledge the support of the Program Pendidikan Magister Menuju Doktor untuk Sarjana Unggul (PMDSU) of the Ministry of Research, Technology and Higher Education of the Republic of Indonesia.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Universitas Indonesia, Depok, Jawa Barat, 16424, Indonesia

    Indra Wibisono,  Yanuar & Engkos A. Kosasih

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  1. Indra Wibisono
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  2. Yanuar
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  3. Engkos A. Kosasih
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Correspondence to Yanuar.

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The research was fully supported by Publikasi Terindeks Internasional (PUTI) Q1 of Universitas Indonesia, under Grant No. NKB-1412/UN2.RST/HKP.05.00/2020.

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Wibisono, I., Yanuar & Kosasih, E.A. Fifth-Order Hermite Targeted Essentially Non-oscillatory Schemes for Hyperbolic Conservation Laws. J Sci Comput 87, 69 (2021). https://doi.org/10.1007/s10915-021-01485-0

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