Volume 43 Issue 7
Jul.  2022
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WANG Yahui. An Improved 3rd-Order WENO Scheme Based on a New Reference Smoothness Indicator[J]. Applied Mathematics and Mechanics, 2022, 43(7): 802-815. doi: 10.21656/1000-0887.420194
 Citation: WANG Yahui. An Improved 3rd-Order WENO Scheme Based on a New Reference Smoothness Indicator[J]. Applied Mathematics and Mechanics, 2022, 43(7): 802-815.

# An Improved 3rd-Order WENO Scheme Based on a New Reference Smoothness Indicator

##### doi: 10.21656/1000-0887.420194
• Rev Recd Date: 2021-08-22
• Publish Date: 2022-07-15
• In order to meet the requirement of high accuracy and high resolution in computational fluid dynamics (CFD), a new reference smoothness indicator was proposed to reduce the numerical dissipation of the classical 3rd-order weighted essentially non-oscillatory (WENO) scheme. The construction method is different from the classical WENO-Z scheme. It is obtained through the L2-norm approximation of the derivatives of the reconstruction polynomials of the whole global stencil, and the linear combination of the derivatives of the reconstruction polynomials on the candidate sub-stencils. With this calculation method, higher-order reference smoothness indicators can be obtained than the WENO-Z scheme. In addition, different reference smoothness indicators can be obtained by change of the value of free parameter $\varphi$. A series of numerical examples prove the effectiveness of the reference smoothness indicator.

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