A flexible framework of high-order shock-capturing schemes for convection-dominated problem

In this work, we further extend the TENO framework proposed by Fu [Fu et al., Journal of Computational Physics 305 (2016): 333-359] with flexibility to control the nonlinear dissipation property of TENO schemes in nonsmooth regions while maintaining the performance of TENO in smooth regions. While a set of candidate stencils of incremental width is constructed, each one is indicated as smooth or nonsmooth by the ENO-like stencil selection procedure proposed in TENO scheme. Rather than being discarded directly in TENO schemes, the nonsmooth candidates are filtered by an extra nonlinear limiter, e.g. monotonicity-preserving (MP) limiter. Consequently, the high-order reconstruction is achieved by assembling the candidate fluxes with the optimal linear weights since they are either smooth reconstructions or filtered ones which feature good non-oscillation property. Based on the proposed framework, several new six- and eight-points TENO schemes with controllable dissipation are developed. A set of critical benchmark cases reveal that the proposed new TENO schemes capture the discontinuities sharply and resolve the high-wavenumber fluctuations with low dissipation, while maintaining the desired accuracy order in smooth regions.