保号WENO-AO型中心迎风格式  

Sign Preserving WENO⁃AO⁃type Central Upwind Schemes

作　　者：郑素佩[1] 建芒芒 封建湖[1] 翟梦情 ZHENG Supei;JIAN Mangmang;FENG Jianhu;ZHAI Mengqing(School of Science,Chang’an University,Xi’an,Shaanxi 710064,China)

机构地区：[1]长安大学理学院,陕西西安710064

出　　处：《计算物理》2022年第6期677-686,共10页Chinese Journal of Computational Physics

基　　金：国家自然科学基金(11971075);陕西省自然科学基金青年项目(2020JQ-338,2020JQ-342)资助

摘　　要：证明Weighted Essentially Non-Oscillatory with Adaptive Order(WENO-AO)重构的保号性,确保在单元交界面处重构值的跳跃符号与原始值的跳跃符号保持一致,给出保号性成立的充分条件。WENO-AO重构通过高阶多项式与低阶重构的非线性组合来实现自适应收敛阶,在求解不连续点附近的解时,WENO-AO重构比经典WENO重构更精确,且具有很好的稳定性。采用中心迎风数值通量,结合时间方向的三阶强稳定Runge-Kutta法计算。数值结果表明该格式最高可达五阶精度,且具有分辨率高、鲁棒性强等良好特性,并能够准确地捕捉间断位置,有效抑制伪振荡的产生。In this paper we give a sufficient condition for sign preservation in Weighted Essentially Non⁃Oscillatory with Adaptive Order(WENO⁃AO)reconstruction,which means to keep same sign for jumping at interfaces.WENO⁃AO reconstruction realizes self⁃adaptive accuracy through an nonlinear combination of high⁃order polynomial and low⁃order reconstruction.In solving solution near discontinuous points,WENO⁃AO reconstruction is more accurate than the classical WENO reconstruction,and it keeps good stability.The scheme is obtained by combining a central upwind numerical flux with a third⁃order strongly stable Runge⁃Kutta method.Numerical results show that the scheme has fifth order accuracy.It has characteristics of high resolution and strong robustness.It captures accurately discontinuous positions and avoids effectively the generation of spurious oscillation.

关 键 词：保号性 WENO-AO重构 双曲守恒律方程 中心迎风通量函数 

分 类 号：O354[理学—流体力学] O241.82[理学—力学]