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A simple method of depressing numerical dissipation effects during wave simulation within the Euler model

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Abstract

Numerical wave tanks are widely-acknowledged tools in studying waves and wave-structure interactions. They can generate waves under realistic scales and offers more information on the fluid field. However, most numerical wave tanks suffer from issues known as the numerical dissipation and numerical dispersion. The former causes wave energy to be slowly dissipated and the latter shifts wave frequencies during wave propagation. This paper proposes a simple method of depressing numerical dissipation effects on the basis of solving Euler equations using the finite difference method (FDM). The wave propagation solutions are solved analytically taking into account the influence of the damping terms. The main idea of the method is to append a source term to the momentum equation, whose strength is determined by how strong the numerical damping effect is. The method is verified by successfully depressing numerical effects during the simulation of regular linear waves, Stokes waves and irregular waves. By applying the method, wave energy is able to be close to its initial value after long distance of travel.

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References

  • Abbasnia A, Ghiasi M. 2015. Fully nonlinear wave interaction with an array of truncated barriers in three dimensional numerical wave tank. Engineering Analysis with Boundary Elements, 58: 79–85, doi: https://doi.org/10.1016/j.enganabound.2015.03.015

    Article  Google Scholar 

  • Abbasnia A, Ghiasi M, Abbasnia A. 2017. Irregular wave transmission on bottom bumps using fully nonlinear NURBS numerical wave tank. Engineering Analysis with Boundary Elements, 82: 130–140

    Article  Google Scholar 

  • Abbasnia A, Soares C G. 2018. Transient fully nonlinear ship waves using a three-dimensional NURBS numerical towing tank. Engineering Analysis with Boundary Elements, 91: 44–49, doi: https://doi.org/10.1016/j.enganabound.2018.03.011

    Article  Google Scholar 

  • Alvarado-Rodríguez C E, Klapp J, Sigalotti L D G, et al. 2017. Nonreflecting outlet boundary conditions for incompressible flows using SPH. Computers & Fluids, 159: 177–188

    Article  Google Scholar 

  • Anbarsooz M, Passandideh-Fard M, Moghiman M. 2013. Fully nonlinear viscous wave generation in numerical wave tanks. Ocean Engineering, 59: 73–85, doi: https://doi.org/10.1016/j.oceaneng.2012.11.011

    Article  Google Scholar 

  • Beljadid A, LeFloch P G, Mishra S, et al. 2017. Schemes with well-controlled dissipation. hyperbolic systems in nonconservative form. Communications in Computational Physics, 21(4): 913–946

    Article  Google Scholar 

  • Bihs H, Kamath A, Chella M A, et al. 2016. A new level set numerical wave tank with improved density interpolation for complex wave hydrodynamics. Computers & Fluids, 140: 191–208

    Article  Google Scholar 

  • Cao Zhiwei, Liu Zhifeng, Wang Xiaohong, et al. 2017. A dissipationfree numerical method to solve one-dimensional hyperbolic flow equations. International Journal for Numerical Methods in Fluids, 85(4): 247–263, doi: https://doi.org/10.1002/fld.4383

    Article  Google Scholar 

  • Daubechies I. 1992. Ten Lectures on Wavelets. Philadelphia, PA: Society for Industrial and Applied Mathematics

    Book  Google Scholar 

  • De Paulo G S, Tomé M F, McKee S. 2007. A marker-and-cell approach to viscoelastic free surface flows using the PTT model. Journal of Non-Newtonian Fluid Mechanics, 147(3): 149–174, doi: https://doi.org/10.1016/j.jnnfm.2007.08.003

    Article  Google Scholar 

  • Dean R G, Dalrymple R A. 1991. Water Wave Mechanics for Engineers & Scientists (Vol. 2). Singapore: World Scientific Publishing Company

  • Elhanafi A, Macfarlane G, Fleming A, et al. 2017. Experimental and numerical measurements of wave forces on a 3D offshore stationary OWC wave energy converter. Ocean Engineering, 144: 98–117, doi: https://doi.org/10.1016/j.oceaneng.2017.08.040

    Article  Google Scholar 

  • Ferziger J H, Peric M. 2012. Computational Methods for Fluid Dynamics. Berlin Heidelberg: Springer

    Google Scholar 

  • Hasan S A, Sriram V, Selvam R P. 2018. Numerical modelling of windmodified focused waves in a numerical wave tank. Ocean Engineering, 160: 276–300, doi: https://doi.org/10.1016/j.oceaneng.2018.04.044

    Article  Google Scholar 

  • Hu Zhe, Tang Wenyong, Xue Hongxiang, et al. 2015. Numerical simullations using conserved wave absorption applied to Navier–Stokes equation model. Coastal Engineering, 99: 15–25, doi: https://doi.org/10.1016/j.coastaleng.2015.02.007

    Article  Google Scholar 

  • Hu Zhe, Tang Wenyong, Xue Hongxiang, et al. 2017. Numerical study of rogue wave overtopping with a fully-coupled fluid-structure interaction model. Ocean Engineering, 137: 48–58, doi:10.1016/j.oceaneng.2017.03.022

    Article  Google Scholar 

  • Hu Zhe et al. Acta Oceanol. Sin., 2020, Vol. 39, No. 1, P. 141–156 155 10.1016/j.oceaneng.2017.03.022

    Google Scholar 

  • Li Zhao, Zhang Yufei, Chen Haixin. 2015. A low dissipation numerical scheme for implicit large eddy simulation. Computers & Fluids, 117: 233–246

    Article  Google Scholar 

  • Liu Xin, Lin Pengzhi, Shao Songdong. 2015. ISPH wave simulation by using an internal wave maker. Coastal Engineering, 95: 160–170, doi: https://doi.org/10.1016/j.coastaleng.2014.10.007

    Article  Google Scholar 

  • Ma Z H, Causon D M, Qian L, et al. 2016. Numerical investigation of air enclosed wave impacts in a depressurised tank. Ocean Engineering, 123: 15–27, doi: https://doi.org/10.1016/j.oceaneng.2016.06.044

    Article  Google Scholar 

  • Nazari F, Mohammadian A, Charron M. 2015. High-order low-dissipation low-dispersion diagonally implicit Runge–Kutta schemes. Journal of Computational Physics, 286: 38–48, doi: https://doi.org/10.1016/j.jcp.2015.01.020

    Article  Google Scholar 

  • Panicker P G, Goel A, Iyer H R. 2015. Numerical modeling of advancing wave front in dam break problem by incompressible navier-stokes solver. Aquatic Procedia, 4: 861–867, doi: https://doi.org/10.1016/j.aqpro.2015.02.108

    Article  Google Scholar 

  • Park J C, Uno Y, Sato T, et al. 2004. Numerical reproduction of fully nonlinear multi-directional waves by a viscous 3D numerical wave tank. Ocean Engineering, 31(11–12): 1549–1565

    Article  Google Scholar 

  • Saincher S, Banerjeea J. 2015. Design of a numerical wave tank and wave flume for low steepness waves in deep and intermediate water. Procedia Engineering, 116: 221–228, doi: https://doi.org/10.1016/j.proeng.2015.08.394

    Article  Google Scholar 

  • Schillaci E, Jofre L, Balcázar N, et al. 2016. A level-set aided singlephase model for the numerical simulation of free-surface flow on unstructured meshes. Computers & Fluids, 140: 97–110

    Article  Google Scholar 

  • Schranner F S, Domaradzki J A, Hickel S, et al. 2015. Assessing the numerical dissipation rate and viscosity in numerical simulations of fluid flows. Computers & Fluids, 114: 84–97

    Article  Google Scholar 

  • Soares D Jr. 2019. A simple explicit-implicit time-marching technique for wave propagation analysis. International Journal of Computational Methods, 16(1): 1850082, doi: https://doi.org/10.1142/S0219876218500822

    Article  Google Scholar 

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Authors and Affiliations

  1. Key Laboratory of Ships and Ocean Engineering of Fujian Province, School of Marine Engineering, Jimei University, Xiamen, 361021, China

    Zhe Hu, Xiaoying Zhang, Weicheng Cui, Xiaowen Li & Yan Li

  2. Deep Sea Technology Research Center, School of Engineering, West Lake University, Hangzhou, 310024, China

    Weicheng Cui

  3. Hadal Science and Technology Research Center, College of Marine Sciences, Shanghai Ocean University, Shanghai, 201306, China

    Weicheng Cui & Fang Wang

Authors
  1. Zhe Hu
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  2. Xiaoying Zhang
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  3. Weicheng Cui
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  4. Fang Wang
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  5. Xiaowen Li
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  6. Yan Li
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Corresponding author

Correspondence to Xiaoying Zhang.

Additional information

Foundation item: The National Natural Science Foundation of China under contract No. 51609101 and 51909103; the Natural Science Foundation of Fujian Province of China under contract Nos 2017J01701, 2017J05085 and 2018J05090; the Outstanding Young University Scientific Research Talents Cultivation Plan of Fujian Province of China.

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Hu, Z., Zhang, X., Cui, W. et al. A simple method of depressing numerical dissipation effects during wave simulation within the Euler model. Acta Oceanol. Sin. 39, 141–156 (2020). https://doi.org/10.1007/s13131-019-1524-1

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  • DOI: https://doi.org/10.1007/s13131-019-1524-1

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