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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