Numerical simulation of wave pattern with variational multiscale method

Liu Xiaogang; Ren Ruichao; Wang Zhen; Hui Xiaojian; Zhang Peijun

doi:10.3969/j.issn.0253-4193.2020.11.004

Volume 42 Issue 11

Dec. 2020

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Liu Xiaogang，Ren Ruichao，Wang Zhen, et al. Numerical simulation of wave pattern with variational multiscale method[J]. Haiyang Xuebao，2020, 42(11)：34–38 doi: 10.3969/j.issn.0253-4193.2020.11.004

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Numerical simulation of wave pattern with variational multiscale method

doi: 10.3969/j.issn.0253-4193.2020.11.004

1.
School of Science, Xijing University, Xi’an 710123, China
2.
School of Mathematics, Northwest University, Xi’an 710127, China

Received Date: 2018-10-09
Rev Recd Date: 2019-09-05

Available Online: 2020-12-23

Publish Date: 2020-11-25

Abstract

Abstract

For the wave model, we combine the variational multiscale method with the free surface captured technology, and decompose various physical quantities of the wave model into “coarse” scale and “fine” scale following the variational multiscale method, and introduce the stabilization structure to eliminate numerical pseudo oscillation. Finally, the total variational multiscale equation of coupling “coarse” scale and “fine” scale is solved to simulate the water wave oscillating freely in a cycle and wave propagation. The numerical results show that the numerical results is accurate, and the method eliminates the spurious oscillations, and simulate correctly the phenomenon of periodic changes of water waves oscillating freely and wave propagation.
- wave model,
- variational multiscale,
- stabilized methods,
- free surface

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References(10)

References

[1]	丁磊, 于博. SWAN模型中不同风拖曳力系数对风浪模拟的影响[J]. 海洋学报, 2017, 39(11): 14−23. Ding Lei, Yu Bo. Impact of wind drag coefficients on wave simulation using SWAN mode[J]. Haiyang Xuebao, 2017, 39(11): 14−23.
[2]	赵红军, 焦影霞, 孔俊. 强非线性和色散性Boussinesq方程数值模型检验[J]. 海洋学报, 2017, 39(5): 10−21. Zhao Hongjun, Jiao Yingxia, Kong Jun. Numerical validation of a Boussinesq-type model for highly nonlinear and dispersive waves[J]. Haiyang Xuebao, 2017, 39(5): 10−21.
[3]	Nachbin A, Milewski P A, Bush J W M. Tunneling with a hydrodynamic pilot-wave model[J]. Physical Review Fluids, 2017, 2(3): 034801. doi: 10.1103/PhysRevFluids.2.034801
[4]	Agapitov O V, Mourenas D, Artemyev A V, et al. Synthetic empirical chorus wave model from combined van allen probes and cluster statistics[J]. JGR Space Physics, 2018, 123(1): 297−314.
[5]	Żyliński M, Niewiadomski W, Sadowiec M, et al. Different methods of arterial compliance estimation tested with reservoir-wave model of arterial system[M]//Lhotska L, Sukupova L, Lacković I, et al. World Congress on Medical Physics and Biomedical Engineering. Singapore: Springer, 2019.
[6]	Langtangen H P, Mardal K A, Winther R. Numerical methods for incompressible viscous flow[J]. Advances in Water Resources, 2002, 25(8/12): 1125−1146.
[7]	Hughes T J R. Multiscale phenomena: green’s functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods[J]. Computer Methods in Applied Mechanics and Engineering, 1995, 127(1/4): 387−401.
[8]	Hughes T J R, Feijóo G R, Mazzei M, et al. The variational multiscale method—a paradigm for computational mechanics[J]. Computer Methods in Applied Mechanics and Engineering, 1998, 166(1/2): 3−24.
[9]	Zienkiewicz O C, Taylor R L. The Finite Element Method Volume 3: Fluid Dynamics[M]. 5th ed. Singapore: Elsevier Pte Ltd., 2004.
[10]	Masud A, Khurram R A. A multiscale/stabilized finite element method for the advection-diffusion equation[J]. Computer Methods in Applied Mechanics and Engineering, 2004, 193(21/22): 1997−2018.