CCWENO型高阶熵稳定格式的保平衡性  

Well-balanced Preserving of CCWENO-type High Order Entropy Stable Schemes for Shallow Water Equations

作　　者：刘沙沙 郑素佩[1] 张成治 封建湖[1] LIU Shasha;ZHENG Supei;ZHANG Chengzhi;FENG Jianhu(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》2024年第4期453-462,共10页Chinese Journal of Computational Physics

基　　金：国家自然科学基金(11971075、12101073)资助项目。

摘　　要：针对带源项的底部非平坦浅水波方程,本文对高阶紧致中心加权基本无振荡(CCWENO)型熵稳定格式的保平衡性进行研究,证明了格式的保平衡性,通过一维和二维数值算例进行验证。数值结果表明:高阶CCWENO型熵稳定格式具有保平衡性,即便在较粗网格下也能够准确捕捉解的微小扰动。The shallow water equations with source term have steady-state solution.The numerical scheme for solving this kind of equations must have well-balanced property,otherwise it will cause oscillation.For the bottom-non-flat shallow water with source term,this paper studies the well-balanced property of the high order compact central weighted essentially non-oscillatory(CCWENO)entropy stable scheme,and proves its well-balanced property.The theory is verified by one-and two-dimensional numerical examples.The numerical results show that the high order CCWENO scheme has the well-balanced property and can accurately capture the small perturbation of the solution even based on the coarse grid.

关 键 词：保平衡性 熵稳定格式 浅水波方程 CCWENO重构 静水稳态 

分 类 号：O354[理学—流体力学] O241.82[理学—力学]