High-order well-balanced methods for systems of balance laws: a control-based approach
作者：
Highlights：
• A general strategy to design high-order well-balanced finite volume methods is introduced.
• Stationary solutions with given averages have to be found at every cell in the reconstruction procedure.
• The key idea is to solve these local problems by using techniques of the control theory.
• The strategy is applied to some 1d systems of balance laws including the shallow water equations.
• Accurate methods that preserve moving stationary solutions for Euler equations with gravity are obtained.
摘要
•A general strategy to design high-order well-balanced finite volume methods is introduced.•Stationary solutions with given averages have to be found at every cell in the reconstruction procedure.•The key idea is to solve these local problems by using techniques of the control theory.•The strategy is applied to some 1d systems of balance laws including the shallow water equations.•Accurate methods that preserve moving stationary solutions for Euler equations with gravity are obtained.
论文关键词：Systems of balance laws,Well-balanced methods,Finite volume methods,High order methods,Reconstruction operators,Euler equations
论文评审过程：Received 13 November 2019, Revised 24 August 2020, Accepted 14 November 2020, Available online 14 December 2020, Version of Record 14 December 2020.
论文官网地址：https://doi.org/10.1016/j.amc.2020.125820
