求解双曲守恒律方程的三阶修正模板WENO格式  

A 3rd-Order Modified Stencil WENO Scheme for Solution of Hyperbolic Conservation Law Equations

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2期224-236,共13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：为了降低经典的三阶加权本质无振荡(WENO)格式的数值耗散,提出了一种新的三阶WENO格式的修正模板近似方法.改进了经典WENO-JS格式中各候选模板上数值通量的一阶多项式逼近,通过加入二次项使模板逼近达到三阶精度.计算了相应的候选通量,并且通过引入可调函数φ(x),使得新的格式具有ENO性质.最后给出了一系列数值算例,证明了该方法的有效性.In order to reduce the numerical dissipation of the classical 3rd-order weighted essentially non-oscillatory(WENO) scheme, a new modified stencil approximation of the 3rd-order WENO scheme was proposed. The 1st-order polynomial approximation of numerical flux on each candidate stencil in the classical WENO-JS3 scheme was improved,and the quadratic term was added to make the stencil approximation reach the 3rd-order accuracy. The corresponding candidate fluxes were calculated. Moreover, the new scheme has essentially non-oscillatory properties through introduction of tunable function φ(x). A series of numerical examples show the effectiveness of the new method.

关 键 词：双曲守恒律 WENO 修正模板 非线性权 

分 类 号：O357.41[理学—流体力学]