TY - JOUR T1 - A Five-Point TENO Scheme with Adaptive Dissipation Based on a New Scale Sensor AU - Huang , Haohan AU - Liang , Tian AU - Fu , Lin JO - Communications in Computational Physics VL - 4 SP - 1106 EP - 1131 PY - 2023 DA - 2023/05 SN - 33 DO - http://doi.org/10.4208/cicp.OA-2022-0286 UR - https://global-sci.org/intro/article_detail/cicp/21671.html KW - TENO, WENO, PDEs, hyperbolic conservation laws, low-dissipation schemes. AB -

In this paper, a new five-point targeted essentially non-oscillatory (TENO) scheme with adaptive dissipation is proposed. With the standard TENO weighting strategy, the cut-off parameter $C_T$ determines the nonlinear numerical dissipation of the resultant TENO scheme. Moreover, according to the dissipation-adaptive TENO5-A scheme, the choice of the cut-off parameter $C_T$ highly depends on the effective scale sensor. However, the scale sensor in TENO5-A can only roughly detect the discontinuity locations instead of evaluating the local flow wavenumber as desired. In this work, a new five-point scale sensor, which can estimate the local flow wavenumber accurately, is proposed to further improve the performance of TENO5-A. In combination with a hyperbolic tangent function, the new scale sensor is deployed to the TENO5-A framework for adapting the cut-off parameter $C_T,$ i.e., the local nonlinear dissipation, according to the local flow wavenumber. Overall, sufficient numerical dissipation is generated to capture discontinuities, whereas a minimum amount of dissipation is delivered for better resolving the smooth flows. A set of benchmark cases is simulated to demonstrate the performance of the new TENO5-A scheme.