求解双曲守恒律的修正模板近似的五阶WENO格式  

Fifth-order modified stencil WENO schemes for hyperbolic conservation laws

作　　者：郭城 王亚辉 GUO Cheng;WANG Ya-hui(Mathematics Department,School of Mathematics and Statistics,Zhengzhou Normal University,Zhengzhou 450044,China)

机构地区：[1]郑州师范学院数学与统计学院数学系,郑州450044

出　　处：《计算力学学报》2024年第3期564-571,共8页Chinese Journal of Computational 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)资助.

摘　　要：针对经典的五阶加权本质无振荡(WENO)格式在间断附近耗散过大以及临界点不能保精度的问题,本文提出了一种新的修正模板近似方法。改进了经典五阶WENO-JS格式中各候选子模板上数值通量的二阶多项式逼近,通过加入三次修正项使模板逼近达到四阶精度,并且通过引入可调函数φ使得新的格式具有ENO性质,理论分析新的格式具有保精度特性,通过一系列数值算例说明了新格式的高效性。In order to solve the problems of the classical fifth-order weighted essentially non-oscillatory(WENO)scheme,such as the excessive dissipation near the discontinuity and the inaccurate preserving of the critical point,a new modified stencil approximation method is proposed.The second-order polynomial approximation of the numerical flux on each candidate sub-stencil in the classical fifth-order WENO-JS scheme is improved,and the stencil approximation reaches the fourth-order accuracy by adding a cubic correction term.The new scheme has ENO property by introducing adjustable functionφ,and the theoretical analysis shows that the new scheme has accuracy-preserving property.A series of numerical examples show the efficiency of the new scheme.

关 键 词：双曲守恒律 WENO 修正模板 非线性权 

分 类 号：O242.1[理学—计算数学]