基于新的参考光滑性指示子的改进的三阶WENO格式  

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

作　　者：王亚辉 WANG Yahui(School of Mathematics and Statistics,Zhengzhou Normal University,Zhengzhou 450044,P.R.China)

机构地区：[1]郑州师范学院数学与统计学院,郑州450044

出　　处：《应用数学和力学》2022年第7期802-815,共14页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(12071470);河南省高等学校重点科研项目(22B110020)。

摘　　要：针对计算流体力学对高精度高分辨率的需求,基于降低经典的三阶加权本质无振荡(WENO)格式的数值耗散特性,该文提出了一种新的参考光滑性指示子.其构造方法与经典的WENO-Z格式不同,它是通过候选子模板上重构多项式的导数的线性组合与整个全局模板上重构多项式的导数的L^(2)范数逼近获得的.采用该计算方法可以得到比WENO-Z格式更高阶的参考光滑性指示子,另外改变自由参数φ的取值,可以获得不同的参考光滑性指示子.该文通过一系列数值算例证明了该参考光滑性指示子的有效性.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 L^(2)-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 φ. A series of numerical examples prove the effectiveness of the reference smoothness indicator.

关 键 词：双曲守恒律 WENO 重构多项式 L^(2)范数 非线性权 

分 类 号：O357.4[理学—流体力学]