Improved discontinuity-resolving scheme with stringent discontinuity-detection criterion for compressible flow simulations

To capture strong discontinuities sharply and resolve multi-scale vortex structures with high-resolution, a hybrid shock-capturing scheme, dubbed the TENO5-THINC scheme, is proposed by combining the standard targeted essentially non-oscillatory (TENO) scheme for smooth flow regions with the tangent of a hyperbola for interface capturing (THINC) reconstruction for non-smooth flow discontinuities. A key step in developing the TENO5-THINC scheme lies in the proposal of a discontinuity-detection criterion for isolating strong discontinuities. However, when increasing the slope parameter to further boost performance, this criterion may amplify the scheme's anti-diffusion property, causing numerical instability. To address this issue, a new discontinuity-resolving scheme is proposed in this work for compressible flow simulations based on two key concepts: (1) a more stringent and compact discontinuity-detection criterion is constructed to reduce misjudgments caused by redundant stencil information, thus accommodating the need for capturing sharper discontinuities; (2) based on the theoretical relationship between the slope parameter and the mesh cell number crossed by discontinuities, the slope parameter in the THINC reconstruction is increased correspondingly to enhance its effectiveness in capturing discontinuities. Numerical results demonstrate that, compared with the standard TENO5-THINC scheme, the improved scheme effectively overcomes the anti-diffusion issue encountered when a large slope parameter is used. Moreover, it captures strong discontinuities more sharply and achieves significantly higher resolution for small-scale vortex structures near discontinuities.