Volume 20, Issue 4
Numerical Studies of 2D Free Surface Waves with Fixed Bottom

Ping Wen Zhang & Xiao Ming Zheng

DOI:

J. Comp. Math., 20 (2002), pp. 391-412

Published online: 2002-08

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  • Abstract

The motion of surface waves under the effect of bottom is a very interesting and challenging phenomenon in the nature, we use boundary integral method to compute and analyze this problem. In the linear analysis, the linearized equations have bounded error increase under some compatible conditions. This contributes to the cancellation of instable Kelvin-Helmholtz terms. Ynder the effect of bottom, the existence of equations is hard to determine, but given some limitations it proves true. These limitations are that the swing of interfaces should be small enough, and the distance between surface and bottom should be large enough. IN order to maintain the stability of computation, some compatible relationship must be satisfied like that of [5]. In the numerical examples, the simulation of standing waves and breaking waves are calculated. And in the case of shallow bottom, we found that the behavior of waves are rather singular.

  • Keywords

Fixed bottom 2D surface wave Boundary integral method Linear analysis Energy analysis

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@Article{JCM-20-391, author = {}, title = {Numerical Studies of 2D Free Surface Waves with Fixed Bottom}, journal = {Journal of Computational Mathematics}, year = {2002}, volume = {20}, number = {4}, pages = {391--412}, abstract = { The motion of surface waves under the effect of bottom is a very interesting and challenging phenomenon in the nature, we use boundary integral method to compute and analyze this problem. In the linear analysis, the linearized equations have bounded error increase under some compatible conditions. This contributes to the cancellation of instable Kelvin-Helmholtz terms. Ynder the effect of bottom, the existence of equations is hard to determine, but given some limitations it proves true. These limitations are that the swing of interfaces should be small enough, and the distance between surface and bottom should be large enough. IN order to maintain the stability of computation, some compatible relationship must be satisfied like that of [5]. In the numerical examples, the simulation of standing waves and breaking waves are calculated. And in the case of shallow bottom, we found that the behavior of waves are rather singular. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8927.html} }
TY - JOUR T1 - Numerical Studies of 2D Free Surface Waves with Fixed Bottom JO - Journal of Computational Mathematics VL - 4 SP - 391 EP - 412 PY - 2002 DA - 2002/08 SN - 20 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8927.html KW - Fixed bottom KW - 2D surface wave KW - Boundary integral method KW - Linear analysis KW - Energy analysis AB - The motion of surface waves under the effect of bottom is a very interesting and challenging phenomenon in the nature, we use boundary integral method to compute and analyze this problem. In the linear analysis, the linearized equations have bounded error increase under some compatible conditions. This contributes to the cancellation of instable Kelvin-Helmholtz terms. Ynder the effect of bottom, the existence of equations is hard to determine, but given some limitations it proves true. These limitations are that the swing of interfaces should be small enough, and the distance between surface and bottom should be large enough. IN order to maintain the stability of computation, some compatible relationship must be satisfied like that of [5]. In the numerical examples, the simulation of standing waves and breaking waves are calculated. And in the case of shallow bottom, we found that the behavior of waves are rather singular.
Ping Wen Zhang & Xiao Ming Zheng. (1970). Numerical Studies of 2D Free Surface Waves with Fixed Bottom. Journal of Computational Mathematics. 20 (4). 391-412. doi:
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