Smoothness indicator is an essential part of weighted essentially non-oscillatory (WENO) scheme, whose target is to distinguish discontinuous profiles and continuous profiles. However, the magnitudes of most of the smoothness indicators will be decreased significantly when the stencil approaches critical points, which would be negative for the numerical simulation. The reason should be that the first derivative term which will drop to almost zero occupies a large proportion in these smoothness indicators. To decrease the variances on different stencils in smooth region, smoothness indicators could be required to be constant for a specific kind of smooth functions, and the best choice should be the sine functions. In the present paper, a new smoothness indicator on four-point stencil is constructed based on this criterion. Compared with the classical smoothness indicator (Jiang and Shu, 1996, [3]), the new one has a more succinct form, and takes less floating point operations which means that it will be more time efficient in the computation. Furthermore, the new smoothness indicator will get a larger variation as the sub-stencil moves from a smooth profile to a discontinuous profile, which would be helpful for stability near discontinuities. By using the new smoothness indicator, a seven-point WENO scheme is constructed which will reduce to the underlying linear scheme for monochromatic waves. As a result, it behaves the same as the underlying linear scheme for approximate dispersion relation (ADR). According to properties of the proposed smoothness indicator, this scheme should have excellent performance for profiles close to sine waves, better stability near discontinuities, and higher time efficiency. Numerical simulations predict the good performance of the proposed scheme.

平滑度指示器是加权基本非振荡（WENO）方案的重要组成部分，其目标是区分不连续轮廓和连续轮廓。但是，当模板接近临界点时，大多数平滑度指标的大小将显着降低，这对于数值模拟将是负面的。原因应该是将下降到几乎为零的一阶导数项在这些平滑度指标中占很大的比例。为了减少平滑区域中不同模板上的差异，对于一种特定的平滑函数，可能要求平滑度指示器恒定，而最佳选择应该是正弦函数。在此基础上，构建了一种新的四点模板光滑度指标。与经典平滑度指标（Jiang和Shu，1996，[3]）相比，新的平滑度指标更简洁，并且浮点运算更少，这意味着它在计算上会更省时。此外，随着子模板从平滑轮廓移动到不连续轮廓，新的平滑度指示器将出现较大的变化，这将有助于在不连续处附近保持稳定性。通过使用新的平滑度指示器，构建了七点WENO方案，该方案将简化为用于单色波的基本线性方案。结果，它的行为与用于近似色散关系（ADR）的基本线性方案相同。根据拟议的平滑度指示器的特性，该方案对于接近正弦波的轮廓应具有出色的性能，不连续点附近的稳定性更好，时间效率更高。数值模拟预测了该方案的良好性能。