An adaptive artificial viscosity for the displacement shallow water wave equation  

作　　者：Keqi YE Yuelin ZHAO Feng WU Wanxie ZHONG 

机构地区：[1]State Key Laboratory of Structural Analysis of Industrial Equipment,Department of Engineering Mechanics,Faculty of Vehicle Engineering and Mechanics,Dalian University of Technology,Dalian,Shenyang Province,116023,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2022年第2期247-262,共16页应用数学和力学（英文版）

摘　　要：The numerical oscillation problem is a difficulty for the simulation of rapidly varying shallow water surfaces which are often caused by the unsmooth uneven bottom,the moving wet-dry interface,and so on.In this paper,an adaptive artificial viscosity(AAV)is proposed and combined with the displacement shallow water wave equation(DSWWE)to establish an effective model which can accurately predict the evolution of multiple shocks effected by the uneven bottom and the wet-dry interface.The effectiveness of the proposed AAV is first illustrated by using the steady-state solution and the small perturbation analysis.Then,the action mechanism of the AAV on the shallow water waves with the uneven bottom is explained by using the Fourier theory.It is shown that the AVV can suppress the wave with the large wave number,and can also suppress the numerical oscillations for the rapidly varying bottom.Finally,four numerical examples are given,and the numerical results show that the DSWWE combined with the AAV can effectively simulate the shock waves,accurately capture the movements of wet-dry interfaces,and precisely preserve the mass.

关 键 词：shallow water wave shock wave artificial viscosity DISPLACEMENT spurious oscillation 

分 类 号：O353[理学—流体力学]