一种高精度圆柱形人工边界条件:水-柱体相互作用问题

A HIGH-ACCURACY CYLINDRICAL ARTIFICIAL BOUNDARY CONDITION: WATER-CYLINDER INTERACTION PROBLEM

针对水-柱体动力相互作用问题,提出一种用于模拟无限域水体的圆柱形高精度时域人工边界条件。首先,基于三维可压缩水体的波动方程和边界条件,采用分离变量法建立了时空全局的精确人工边界条件;然后,将其动力刚度表示为外域模型和波导模型人工边界条件动力刚度的嵌套形式;之后,应用时间局部化方法得到时间局部的高精度人工边界条件;最后,离散高精度人工边界条件,并将其与近场有限元方程耦合,形成一种能够采用显式时间积分方法求解的时间二阶常微分方程组。数值算例表明:提出的三维圆柱形高精度人工边界条件精确、高效、稳定。

A high-accuracy cylindrical artificial boundary condition(ABC)for water-cylinder dynamic interaction problem is presented to simulate the truncated infinite domain.Firstly,according to the wave equation and boundary conditions for the three-dimensional compressible water,an exact ABC that is global in time and space is developed by using the method of separation of variables.Secondly,the dynamic-stiffness of the cylindrical ABC is rewritten as a nested form of the two-dimensional linear and circular dynamic-stiffness.Thirdly,a high-accuracy ABC that is local in time but global in space is obtained by applying the temporal localization method.Fourthly,the resulted high-accuracy ABC is discretized using finite element method.Lastly,a symmetric second-order ordinary differential equations in time is developed by coupling the results with the finite element equation of the near field.The finite equation can be solved by explicit time integration algorithm.Numerical example demonstrates that the presented ABC is accurate,efficient and stable.