A Modified TENO Scheme with Improved Efficiency

Fu et al. (J Comput Phys 374:724–751, 2018), a class of adaptive targeted ENO (TENO) schemes have been proposed. Excellent resolution and robustness of the TENO scheme were validated by benchmark problems, but the computational cost is high. In order to improve the computational efficiency, a modified TENO scheme is proposed in this article. First, using the weighting strategy of the fifth-order TENO as an explicit discontinuity detector, locations of discontinuities are detected on the five-point stencil, and the initial target stencil with maximum support on the five-point stencil is obtained. Then, with a simple discontinuity detection strategy, the initial target stencil is enlarged point by point in the direction where no discontinuity is detected. In this manner, final target stencil with maximum support, not crossed by discontinuities, on the full six- or eight-point stencil is formed. Unlike TENO using candidate stencils with incrementally increased width, all stencils are three-point in the new framework. Due to the simplified determination of final target stencil and avoiding expensive calculation of smoothness indicator of large stencil, the computational cost of TENO-M is significantly lower than that of TENO. Several benchmark problems are conducted to validate the performance of the proposed scheme.