Whitham方程的SAV能量守恒型格式  

SAV Energy-Preserving Schemes for the Whitham Equation

作　　者：翟梦姣 陈春光[1] Zhai Mengjiao;Chen Chunguang(School of Mathematical Sciences,Ocean University of China,Qingdao 266100,China)

机构地区：[1]中国海洋大学数学科学学院,山东青岛266100

出　　处：《中国海洋大学学报（自然科学版）》2022年第S01期83-90,共8页Periodical of Ocean University of China

基　　金：山东省自然科学基金项目(ZR2021MA005)资助。

摘　　要：Whitham方程是一种描述无黏流体表面波的微分-积分方程。本文提出了Whitham方程的两种基于标量辅助变量(SAV)方法的能量守恒型数值格式,即SAV龙格-库塔(RK)格式和SAV拉格朗日乘子(LagM)格式。其中SAV-RK是线性格式,可以达到任意阶时间精度;SAV-LagM为二阶时间精度格式,并保持原始能量守恒。本文从理论上证明了两种格式均保持能量守恒。空间离散采用傅里叶拟谱方法。数值结果验证了两种格式的能量守恒性和精度。Whitham equation is a differential-integral equation that models the surface wave of inviscid fluid. We propose two energy-preserving schemes based on the scalar auxiliary variable(SAV) method, namely, the SAV Runge-Kutta(RK) scheme and the SAV Lagrange multiplier(LagM) scheme, for the Whitham equation. The SAV-RK scheme is linear and can reach arbitrarily high order accuracy in time and the SAV-LagM scheme is a second-order time-accuracy scheme that conserves the original energy of the equation. Both methods are theoretically proved to be energy-preserving. The Fourier pseudo-spectral method is applied in spatial discretization. Numerical tests results verify the conservation of energy and accuracy of both methods.

关 键 词：Whitham方程 能量守恒 标量辅助变量方法 龙格-库塔方法 拉格朗日乘子 

分 类 号：O241.82[理学—计算数学] O241.83[理学—数学]