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.

我们提出了一种基于Hermite多项式的有针对性的基本非振荡（TENO）方案，用于解决双曲守恒律。加权基本非振荡（WENO）方案已采用Hermite多项式（Qiu和Shu，J Comput Phys 193：115-135，2003）。与早期的重建相比，Hermite TENO重建具有主要优势。也就是说，它是紧凑的Hermite型重构，并且借助TENO的模版投票策略具有较低的耗散率。接下来，我们为拟议的方案制定了一个新的高阶全局参考平滑度指标。通量计算和时间提前方案分别通过局部Lax–Friedrichs通量和三阶保强稳定性Runge–Kutta方法进行。数值试验证明了双曲守恒律的标量和系统。在这些测试中，提出的方案提高了震动捕获性能，并继承了TENO方案的良好小规模分辨率。