A high-efficiency adaptive TENO scheme with optimal accuracy order for compressible flow simulation

Abstract

In this paper, we propose a new adaptive cut-off function and develop a fifth-order targeted ENO scheme that achieves optimal accuracy at any order of critical points, which performs excellently in conventional compressible gas dynamics. The cut-off value CT is crucial for controlling the dissipation in TENO schemes. Adjusting CT can improve shock capture and increase dissipation for small-scale features. To address this issue, Fu et al. [27] and Peng et al. [28] developed the TENO-A and TENO-LAD schemes, respectively, with adaptive cut-off values CT. However, these adaptive cutoffs CT are computationally expensive due to additional free parameters and complexity. Furthermore, all TENO schemes, including the adaptive versions, can suffer from loss of accuracy at higher-order critical points. In this paper, a new adaptive cut-off function is proposed that uses a global smoothness indicator correction so that it can be automatically tuned between 0 and a given positive constant λd, ensuring that the new TENO scheme achieves optimal accuracy in smooth regions and good shock-capturing in the less smooth parts. A series of benchmark simulations demonstrate that the presented scheme provides optimal accuracy, better robustness, resolution, and numerical stability, and higher resolution than existing TENO schemes while improving computational efficiency. Due to the simplicity of the new cut-off structure, it can be easily extended to improve other TENO schemes.Program files associated to this article may be found at https://github.com/fourhairs/cfd.