Zhe Hu, Xiaoying Zhang, Weicheng Cui, Fang Wang, Xiaowen Li, Yan Li. A simple method of depressing numerical dissipation effects during wave simulation within the Euler model[J]. Acta Oceanologica Sinica, 2020, 39(1): 141-156. doi: 10.1007/s13131-019-1524-1
Citation: Zhe Hu, Xiaoying Zhang, Weicheng Cui, Fang Wang, Xiaowen Li, Yan Li. A simple method of depressing numerical dissipation effects during wave simulation within the Euler model[J]. Acta Oceanologica Sinica, 2020, 39(1): 141-156. doi: 10.1007/s13131-019-1524-1

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

doi: 10.1007/s13131-019-1524-1
Funds:  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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  • Corresponding author: E-mail: zhangxy@jmu.edu.cn
  • Received Date: 2018-08-29
  • Accepted Date: 2019-01-06
  • Available Online: 2020-04-21
  • Publish Date: 2020-01-20
  • 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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  • [1]
    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: 10.1016/j.enganabound.2015.03.015
    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
    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: 10.1016/j.enganabound.2018.03.011
    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
    Anbarsooz M, Passandideh-Fard M, Moghiman M. 2013. Fully nonlinear viscous wave generation in numerical wave tanks. Ocean Engineering, 59: 73–85. doi: 10.1016/j.oceaneng.2012.11.011
    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
    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
    Cao Zhiwei, Liu Zhifeng, Wang Xiaohong, et al. 2017. A dissipation-free numerical method to solve one-dimensional hyperbolic flow equations. International Journal for Numerical Methods in Fluids, 85(4): 247–263. doi: 10.1002/fld.4383
    Daubechies I. 1992. Ten Lectures on Wavelets. Philadelphia, PA: Society for Industrial and Applied Mathematics
    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: 10.1016/j.jnnfm.2007.08.003
    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: 10.1016/j.oceaneng.2017.08.040
    Ferziger J H, Peric M. 2012. Computational Methods for Fluid Dynamics. Berlin Heidelberg: Springer
    Hasan S A, Sriram V, Selvam R P. 2018. Numerical modelling of wind-modified focused waves in a numerical wave tank. Ocean Engineering, 160: 276–300. doi: 10.1016/j.oceaneng.2018.04.044
    Hu Zhe, Tang Wenyong, Xue Hongxiang, et al. 2015. Numerical simulations using conserved wave absorption applied to Navier–Stokes equation model. Coastal Engineering, 99: 15–25. doi: 10.1016/j.coastaleng.2015.02.007
    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
    Li Zhao, Zhang Yufei, Chen Haixin. 2015. A low dissipation numerical scheme for implicit large eddy simulation. Computers & Fluids, 117: 233–246
    Liu Xin, Lin Pengzhi, Shao Songdong. 2015. ISPH wave simulation by using an internal wave maker. Coastal Engineering, 95: 160–170. doi: 10.1016/j.coastaleng.2014.10.007
    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: 10.1016/j.oceaneng.2016.06.044
    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: 10.1016/j.jcp.2015.01.020
    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: 10.1016/j.aqpro.2015.02.108
    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
    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: 10.1016/j.proeng.2015.08.394
    Schillaci E, Jofre L, Balcázar N, et al. 2016. A level-set aided single-phase model for the numerical simulation of free-surface flow on unstructured meshes. Computers & Fluids, 140: 97–110
    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
    Soares D Jr. 2019. A simple explicit-implicit time-marching technique for wave propagation analysis. International Journal of Computational Methods, 16(1): 1850082. doi: 10.1142/S0219876218500822
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