In the present work, we propose a new discontinuity indicator for constructing shock-capturing finite difference schemes based on the self-adaptation algorithm in the WENO-OS4 scheme (Li et al. in J Sci Comput 71:109–143, 2017). The new discontinuity indicator can identify the discontinuities as accurate as the original self-adaptation algorithm through using a more straightforward numerical condition. The high-resolution and the problem-independency of the original algorithm for identifying discontinuities are maintained, but the excessive expenses are greatly reduced by the decoupled implementation and the employment of the local characteristic projection. Moreover, new hybrid WENO schemes are constructed based on this new discontinuity indicator. The hybrids are carried out between nonlinear WENO schemes with shock-capturing ability and linear upwind or central schemes with high resolution. Both the effectiveness of the indicator and the good resolution of the hybrid schemes are demonstrated by the numerical tests. The results of the tests indicate that the new hybrid WENO schemes have significant improvements on both resolution and computational efficiency when compared with the WENO-JS5 and WENO-OS4.

在目前的工作中，我们提出了一种新的不连续性指标，用于基于WENO-OS4方案中的自适应算法构造捕捉震动的有限差分方案（Li等人，J Sci Comput 71：109-143，2017）。通过使用更直接的数值条件，新的不连续性指示器可以识别出与原始自适应算法一样准确的不连续性。保留了用于识别不连续性的原始算法的高分辨率和问题独立性，但是通过解耦的实现和局部特征投影的使用大大减少了过多的开销。此外，基于此新的不连续性指标构造了新的混合WENO方案。在具有震荡能力的非线性WENO方案与高分辨率的线性迎风或中心方案之间进行混合。数值测试证明了指标的有效性和混合方案的良好分辨率。测试结果表明，与WENO-JS5和WENO-OS4相比，新的混合WENO方案在分辨率和计算效率上都有显着提高。