奇异边界法分析含水下障碍物水域中的水波传播问题

研究奇异边界法模拟水波在含水下障碍物水域的传播过程.奇异边界法是一种最近提出的新型边界配点方法，具有无网格和无数值积分、数学简单、编程容易等优点.首先研究了奇异边界法分析典型水波算例的精度及效率，并与边界元法的计算结果进行比较，然后通过数值模拟讨论分析了水下障碍物位置、尺寸及形状等因素对水波传播的影响.发现奇异边界法的计算精度较高，且与边界元法的计算结果吻合较好;数值结果显示水下障碍物的不同高宽比对水波的传播影响明显:障碍物无量纲高度越大对水波的屏障作用越明显；障碍物无量纲宽度增加对水波的屏障作用先增强后变弱.在高宽比一定时,斜率变化对水波的屏障作用不明显；含吸收边界水下障碍物可以得到较低的传递系数和较高的反射系数, 对水波的屏障作用更为明显.

The Singular Boundary Method for Obliquely Incident Water Wave Passing a Submerged Breakwater

The singular boundary method (SBM) was implemented to solve the obliquely incident water wave passing a submerged breakwater. The SBM was a recently emerging boundary-type collocation method with the merits of being meshless, integration-free, mathematically simple and easy-to-program. The accuracy and efficiency of the SBM was first investigated through the benchmark examples in comparison with the boundary element method. Then the effects of the position, size and geometry of the breakwater on the water wave propagation were analyzed through extensive numerical experiments. The numerical results verify that the present SBM provides accurate solutions in good agreement with those of the boundary element method. Then the numerical investigations show that the size of the breakwater has a great effect on the water wave propagation. The larger the dimensionless height of the breakwater is, the more obvious the observed shield effect is on the water wave propagation passing the submerged breakwater. With the increasing dimensionless width of the breakwater, the shield effect of the breakwater first rises and then falls. The slope of the breakwater has no obvious shield effect on the water wave propagation. The absorbing submerged breakwater has smaller transmission coefficient T and larger reflection coefficient R than the rigid submerged breakwater, which means a more obvious shield effect.