一维双曲守恒律方程的保极值间断有限体积元方法  

A Maximum-Principle Satisfying Discontinuous Finite Volume Element Scheme for One-Dimensional Hyperbolic Conservation Laws

作　　者：陈浩 高巍[1] 

机构地区：[1]内蒙古大学数学科学学院,内蒙古 呼和浩特

出　　处：《应用数学进展》2020年第11期1934-1944,共11页Advances in Applied Mathematics

摘　　要：本文利用间断有限体积元方法求解双曲守恒律方程。为克服传统TVD限制器的精度损失问题,本文采用了保极值限制器。时间离散上采用了三阶的SSP Runge-Kutta方法。经典算例结果验证了本方法计算的有效性和精度。In the article, we present a discontinuous finite volume element method for solving hyperbolic conservation laws. A maximum-principle satisfying limiter is adopted to keep accuracy. The time discretization is based on third order SSP Runge-Kutta scheme. Typical test cases show the effectiveness and accuracy of the present scheme.

关 键 词：间断有限体积元方法 斜率限制器 Runge-Kutta时间离散 双曲守恒律 

分 类 号：G63[文化科学—教育学]