A five-point TENO scheme with adaptive dissipation based on a new scale sensor

TL;DR

This paper introduces a new five-point TENO scheme with an adaptive dissipation mechanism based on a novel scale sensor that accurately estimates local flow wavenumber, enhancing discontinuity capturing and smooth flow resolution.

Contribution

A new five-point scale sensor is proposed to improve the TENO5-A scheme's ability to adapt dissipation based on local flow wavenumber, leading to better performance.

Findings

Enhanced discontinuity capturing in benchmark tests

Improved resolution of smooth flows

Effective adaptation of dissipation based on local flow features

Abstract

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.