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An adaptive artificial viscosity for the displacement shallow water wave equation

Applied Mathematics and Mechanics(English Edition) 2022年第2期43卷 247-262页

作者： Keqi YE Yuelin ZHAO Feng WU Wanxie ZHONG State Key Laboratory of Structural Analysis of Industrial Equipment Department of Engineering MechanicsFaculty of Vehicle Engineering and MechanicsDalian University of TechnologyDalianShenyang Province116023China

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 *** 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 *** effectiveness of the proposed AAV is first illustrated by using the steady-state solution and the small perturbation ***,the action mechanism of the AAV on the shallow water waves with the uneven bottom is explained by using the Fourier *** 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 ***,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

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Study of total variation diminishing (TVD) slope limiters in dam-break flow simulation

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Water Science and Engineering 2018年第1期11卷 68-74页

作者： Feng-peng Bai Zhong-hua Yang Wu-gang Zhou State Key Laboratory of Water Resources and Hydropower Engineering Science Wuhan University

A two-dimensional （2D） dam-break flow numerical model was developed based on the finite-volume total variation diminishing （TVD） and monotone upstream-centered scheme for conservation laws （MUSCL）-Hancock scheme, which has second-order accuracy in both time and space. A Harten-Lax-van Leer-contact （HLLC） approximate Riemann solver was used to evaluate fluxes. The TVD MUSCL-Hancock numerical scheme utilizes slope limiters, such as the minmod, double minmod, superbee, van Albada, and van Leer limiters, to prevent spurious oscillations and maintain monotonicity near discontinuities. A comparative study of the impact of various slope limiters on the accuracy of the numerical flow model was conducted with several dam-break examples including wet and dry bed cases. The numerical results of the superbee and double minmod limiters agree better with the theoretical solution and have higher accuracy than other limiters in one-dimensional （1D） space. The ratio of the downstream water depth to the upstream water depth was used to select the proper slope limiter. For the 2D numerical model, the superbee limiter should not be used, owing to significant numerical dispersion.

关键词： Dam-break flow TVD MUSCL-Hancock scheme Slope limiter Numerical accuracy spurious oscillation

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