| Hu Zhe,Zhang Xiaoying,Cui Weicheng,Wang Fang. 2020. A simple method of depressing numerical dissipation effects during wave simulation within the Euler model. Acta Oceanologica Sinica, 39(1):141－156 |
| A simple method of depressing numerical dissipation effects during wave simulation within the Euler model |
| 欧拉模型模拟波浪的抑制数值耗散效应的一种简单方法 |
| Received:August 29, 2018 |
| DOI：10.1007/s13131-019-1524-1 |
| Key words:numerical dissipation numerical wave tank wave simulation numerical damping reduction finite difference method |
| 中文关键词: 数值耗散,数值波浪水槽,波浪模拟,减小数值阻尼,有限差分法 |
| 基金项目: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. |
| Author Name | Affiliation | E-mail | | Hu Zhe | Key Laboratory of Ships and Ocean Engineering of Fujian Province, School of Marine Engineering, Jimei University, Xiamen 361021, China | | | Zhang Xiaoying | Key Laboratory of Ships and Ocean Engineering of Fujian Province, School of Marine Engineering, Jimei University, Xiamen 361021, China | | | Cui Weicheng | Key Laboratory of Ships and Ocean Engineering of Fujian Province, School of Marine Engineering, Jimei University, Xiamen 361021, China
Deep Sea Technology Research Center, School of Engineering, West Lake University, Hangzhou 310024, China
Hadal Science and Technology Research Center, College of Marine Sciences, Shanghai Ocean University, Shanghai 201306, China | zhangxy@jmu.edu.cn | | Wang Fang | Hadal Science and Technology Research Center, College of Marine Sciences, Shanghai Ocean University, Shanghai 201306, China | |
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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. |
| 中文摘要: |
| 数值波浪水槽是研究波浪及波浪与结构相互作用的常用工具，可在真实尺度下产生波浪，并提供流场的详细数据。然而，大部分数值波浪水槽都存在数值耗散和数值色散问题，数值耗散使波能缓慢消散，数值弥散在波传播过程中使波频移。本文在有限差分法（FDM）求解欧拉方程的基础上，提出了一种抑制数值耗散效应的简单方法，考虑阻尼项的影响，对波的传播解进行了解析求解。该方法的主要思想是在动量方程中附加一个源项，其强度由数值阻尼效应的强度决定。本文通过对规则线性波、Stokes波和不规则波的数值模拟，验证了该方法的有效性。结果表明，本文方法可有效减小数值波浪水槽中存在的数值耗散现象。 |
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