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A generating and absorbing boundary condition for dispersive waves in detailed simulations of free-surface flow interaction with marine structures

机译：与海洋结构的自由表面流动相互作用详细模拟分散波的发电和吸收边界条件

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摘要

The boundaries of numerical domains for free-surface wave simulations with marine structures generate spurious wave reflection if no special measures are taken to prevent it. The common way to prevent reflection is to use dissipation zones at the cost of increased computational effort. On many occasions, the size of the dissipation area is considerably larger than the area of interest where wave interaction with the structure takes place. Our objective is to derive a local absorbing boundary condition that has equal performance to a dissipation zone with lower computational cost. The boundary condition is designed for irregular free-surface wave simulations in numerical methods that resolve the vertical dimension with multiple cells. It is for a range of phase velocities, meaning that the reflection coefficient per wave component is lower than a chosen value, say 2%, over a range of values for the dimensionless wave number kh. This is accomplished by extending the Sommerfeld boundary condition with an approximation of the linear dispersion relation in terms of kh, in combination with vertical derivatives of the solution variables. For this article, the boundary condition is extended with a non-zero right-hand side in order to prevent wave reflection, while, at the same time, at the same boundary, generating waves that propagate into the domain. Results of irregular wave simulations are shown to correspond to the analytical reflection coefficient for a range of wave numbers, and to have similar performance to a dissipation zone at a lower cost. (C) 2019 The Author(s). Published by Elsevier Ltd.
机译：如果没有采取特殊措施防止它，则使用船舶结构的自由表面波模拟数值域的边界产生虚假波反射。防止反射的常见方法是以增加计算工作的成本使用耗散区域。在很多场合，耗散区域的尺寸远大于与结构的波浪相互作用的感兴趣区域大大大。我们的目标是导出局部吸收边界条件，其具有较低计算成本的耗散区的性能。边界条件是为在数值方法中的不规则自由表面波模拟而设计，该方法用多个单元解析垂直尺寸。它是一系列相速度，这意味着每个波分量的反射系数低于所选择的值，比如2％，在无量纲波数Kh的值范围内。这是通过延伸Sommerfeld边界条件来实现，其与kh的线性色散关系近似，与溶液变量的垂直衍生物组合。对于本文，边界条件与非零右侧延伸，以防止波反射，同时在同一边界处生成传播到域中的波。不规则波模拟的结果被示出对应于一系列波数的分析反射系数，并且以较低的成本对耗散区具有类似的性能。 （c）2019年作者。 elsevier有限公司出版

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