海洋拖曳系统运动方程的变步长有限差分数值仿真

有限差分算法是常用的海洋拖曳系统运动仿真计算方法,传统的有限差分算法在对拖缆进行离散时,采用固定空间步长,为了提高数值计算的精度,通常需要减小空间步长,这既增加了计算时间,又浪费了计算机内存,甚至造成无法仿真一些工况。针对这一问题,提出了变步长有限差分数值算法,给出了步长变化的设定原则与算法,在建立海洋拖曳系统运动模型的基础上,系统分析了这一方法的求解思想与过程,并分别采用传统固定步长有限差分算法(大空间步长和小空间步长)和变步长有限差分算法,对模型进行了数值仿真,结果表明:变步长有限差分算法不仅保证了仿真计算精度,而且降低了计算机内存需求量,减少了计算时间。此外,变步长有限差分算法具有较高的灵活性,可根据实际情况,综合考虑计算时间、内存需求量和计算结果精度,从而选择合适的空间步长变化规律。

The numerical simulation of underwater towed system using the finite difference method with variational step

The finite difference method is often used in the simulation of underwater towed system. In normal finite difference method, the towed cable is discreted and the step is fixed. In order to enhance the accuracy the simulation result, the step should be small, but the simulation time and requirement of memory in process are large, and even some operation conditions can't be simulation. For this reason, the finite difference method with variational step is proposed to the simulation of underwater towed system. The rule and algorithm of variational step are given out and the equations of towed system are established. Based on these equations, the solving idea and process are put forward. The numerical simulations are implemented using the finite difference method with large step, small step and variational step. The numerical results show that the result of finite difference method with variational step is accurate. Moreover, the computing time and computer memory are reduced. The finite difference method is a method with flexibility and the step can be set according to the computing time, the requirement of memory in process and the accuracy of computed results.