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,...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.展开更多
文摘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.
基金This work was supported by the National Natural Science Foundation of China grants(Grant Nos.U1906233,11472076 and 51609034)the National Key R&D Program of China(Grant No.2021YFA1003501)+2 种基金the Science Foundation of Liaoning Province of China(Grant No.2021-MS-119)the Dalian Youth Science and Technology Star project(Grant No.2018RQ06)the Fundamental Research Funds for the Central Universities grant(Grant No.DUT20GJ216).
