To enhance the performance of the third-order weighted essentially non-oscillatory (WENO) scheme on the four-point stencil, a new hybrid central-type scheme is proposed in this paper. Developments are conducted in the following two aspects. First, a new fourth-order central WENO scheme, named as WENO4-LC, is devised for shock capturing, and a low dissipative third-order grid-centered upwind scheme is adopted for the smooth region. Second, a discontinuity indicator is extended to the four-point stencil version, which is simpler than its counterpart in our former article (Guo et al. in J Sci Comput 83, 28, 2020), for switching between the linear and nonlinear branch of the hybrid scheme. Numerical tests of the Euler and Navier–Stokes benchmarks show that the new indicator is good on detecting the discontinuities. Moreover, the performances of the central-type WENO4-LC and its corresponding hybrid scheme have obvious improvements compared with those of WENO3-JS and WENO3-L, and even behave slightly better than classical WENO5-JS on resolving the fluid structures. Meanwhile, the hybrid scheme is efficient which only costs 76% CPU time of WENO3-JS and about 58% of WENO5-JS.

为了提高三点加权基本非振荡（WENO）方案在四点模板上的性能，提出了一种新的混合中心型方案。在以下两个方面进行开发。首先，设计了一种新的名为WENO4-LC的四阶中央WENO方案来捕获振动，并为光滑区域采用了低耗散的以三阶网格为中心的迎风方案。其次，将不连续性指标扩展到四点模板版本，该模板比我们上一篇文章中的对应版本更简单（Guo等人，J Sci Comput83，28，2020），用于在混合方案的线性和非线性分支之间进行切换。Euler和Navier-Stokes基准的数值测试表明，该新指标可以很好地检测不连续性。而且，与WENO3-JS和WENO3-L相比，中心型WENO4-LC及其对应的混合方案的性能有明显的提高，在解决流体结构方面甚至比传统的WENO5-JS稍好。同时，混合方案效率很高，仅花费WENO3-JS 76％的CPU时间和WENO5-JS 58％的时间。