High-Order Finite-Volume TENO Schemes with Dual ENO-Like Stencil Selection for Unstructured Meshes

The TENO-family schemes (Fu et al. in J Comput Phys 305: 333-359, 2016) have been demonstrated to perform well for compressible gas dynamics and turbulent flow predictions on structured meshes. However, the extension of the TENO schemes to unstructured meshes is non-trivial and challenging, particularly when the multiple design objectives are pursued simultaneously, i.e., restoring the high-order accuracy in smooth regions, retaining the low numerical dissipation for small-scale features, maintaining the sharp shock-capturing property, and featuring the good numerical robustness for high-Mach flows. In this work, a family of very-high-order (up to seventh-order accuracy) robust finite-volume TENO schemes with dual ENO-like stencil selection for unstructuredmeshes is proposed. The stencils include one large stencil and several small stencils. The novelty originates from a so-called dual ENO-like stencil selection strategy. Following a strong scale separation, the ENO-like stencil selection procedure with a small C-T is first enforced among all the candidates such that the high-order candidate scheme on the large stencil is adopted for the final reconstruction when the local flow is smooth. If the large stencil is judged to be crossed by discontinuities, a second ENO-like stencil selection with a relatively large C-T is applied to all the left small stencils and the ENO property is obtained by selecting the smooth small stencils which are not crossed by discontinuities. The smaller C-T in the first stage ensures that the high-order reconstruction is restored for smooth flow scales with higher wavenumbers. On the other hand, the larger C-T in the second stage can enforce a strong nonlinear adaptation for capturing discontinuities with better robustness. Such a dual ENO-like stencil selection strategy introduces an explicit scale separation and deploys the optimal strategy for different types of flows correspondingly. Without parameter tuning, a set of benchmark simulations has been conducted to validate the performance of the proposed TENO schemes. Numerical results demonstrate the good numerical robustness and the low-dissipation property for highly compressible flows with shockwaves.

Automated summary

This study proposes a robust finite-volume TENO scheme for unstructured meshes with up to seventh-order accuracy. The scheme utilizes a dual ENO-like stencil selection strategy to achieve optimal performance for different types of flows while maintaining high-order reconstruction and good robustness. Benchmark simulations demonstrate the good numerical robustness and low-dissipation property of the proposed scheme for highly compressible flows with shockwaves.