Hybrid Hermite TENO scheme with a simple smoothness indicator for compressible flow simulations

The Hermite targeted essentially non-oscillatory (HTENO) scheme offers an excellent small-scale resolution and better shock-capturing capability in solving compressible flow problems. However, the scheme has a high computational cost due to global reference smoothness indicators and artificial limiters. In this paper, we improve the computational efficiency by simplifying the smoothness indicator of the HTENO scheme and adopting a hybrid reconstruction method, where the HTENO scheme is only employed near the discontinuous region and uses linear reconstruction for the smooth parts. The numerical results show that the proposed scheme achieves the desired order of accuracy and inherits HTENO's numerical resolutions while improving the computational efficiency.