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

Indra Wibisono, Yanuar, Engkos A. Kosasih

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12 Citations (Scopus)


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.

Original languageEnglish
Article number69
JournalJournal of Scientific Computing
Issue number3
Publication statusPublished - Jun 2021


  • Finite-volume method
  • High-order schemes
  • Hyperbolic conservation laws
  • Shock-capturing
  • WENO schemes


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