An Improved TENO‐A Scheme With Adaptive Accuracy for Hyperbolic Conservation Laws

ABSTRACT A novel TENO‐adaptive accuracy (TENO‐A) scheme is proposed to perform complex flowfield simulations containing abundant vortex field details and shock wave discontinuities. This hybrid scheme not only enhances the low dissipation property of the TENO scheme in smooth regions but also improves the discontinuity‐resolving capability for shock waves while retaining the robustness of the scheme. A unified and robust discontinuous detector using the information within the global stencil width is applied to separate discontinuous and smooth regions, which is not case and parameter sensitive. In discontinuous regions, the THINC scheme with jump‐like distribution is adopted to well approximate a discontinuity within a grid. Besides, in the smoothest region, the global reconstruction value is adopted as the final reconstruction value, and the accuracy is improved from the original fifth‐order to sixth‐order; in the general smooth region, based on the Kriging method, the candidate stencil reconstruction is employed for final reconstruction with nonlinear weights, which improves the accuracy of the candidate stencil from the original third‐order to fourth‐order. As a result, the dissipation is significantly reduced using both types of reconstruction, which is beneficial to resolve small‐scale flow structures. A set of numerical results demonstrates that the TENO‐A scheme performs better in one‐dimensional and two‐dimensional cases than the standard TENO scheme and is able to predict complex flowfield without the necessity of parameter tuning case by case, and the hybrid scheme can restore high‐order accuracy, maintain low dissipation property, and avoid spurious oscillations.