摘要
对近年来网渔具的计算机数值模拟中使用的几何拓扑分解方法、数学建模思想和模型算法等进行了归纳和系统整理,并探讨了各种算法的稳定性和收敛性。分析认为:刚体有限元法数学建模的优点是模型简化,能基本反映网具粗糙形状,缺点是忽略网线张力,无法精确反映网具的受力和网具的运动状态;基于质量弹簧体系和牛顿力学的柔性有限元法是主流,数值模拟结果更符合网具的实际状况,网形更细腻逼真,计算结果与网具实测拟合较好;显式算法对时间步长较敏感,稳定性和精度不如隐式算法好。NEWTON-RAPHSON和NEWMARK-β算法具有无条件稳定性和收敛性,大部分研究采用了此算法。
The paper summarized and systematized the geometric topological decomposition method,mathematical modeling and algorithm used in numerical computer simulations on fishing nets（ trawl,purse seine）. Research literature related to the use of computer technology and mathematical models to numerically simulate the behavior of fishing nets,the tension distribution and dynamic visualization were reviewed.Currently there is a considerable gap in numerical research and digital design on fishing nets between China and developed fishing courtries,this paper also discussed most of the major ideas of mathematical modeling,complex formulas and computer-implemented methods,and algorithm stability. The purpose is to introduce and study the main international numerical simulation tools and methods,to promote the domestic development of digital fishing nets.The paper introduced and summarized the numerical simulation of fishing nets in computer in five aspects： 1） advances in numerical simulation of fishing nets（ trawl,purse seine）; 2） geometric topological decomposition method of fishing nets; 3） main methods of mathematical modeling; 4） basic methods for solving model; 5） basic simulation results of fishing nets. According to relevant studies,from partial to the whole the numerical simulation of fishing nets can be divided into： numerical simulation of components（ such as netting,ropes,cod end） and the entire fishing net; in the geometric decomposition method of physicalmodels,it can be divided into rigid finite element method and flexible finite element method,lumped mass method,and mass-spring system. There are basically three categories in mathematical modeling methods：Newtonian mechanics method,the energy conservation law,and rigid finite element method; the main mathematical model solving methods were： finite difference method, NEWTON-RAPHSON method,NEWMARK-β method, RUNGE-KUTTA method, and finite element algorithm. And the stability and convergence of different algorithms were analyzed by a simple example.Early rigid finite element method ignored the internal tension within net line,the netting was seen as a finite number of units connected by a rigid solid object,so the shape of fishing net solved by this method was relatively stiff and rough,it was a rough description of the basic shape of a fishing gear（ Fig. 7）. The calculation of rigid finite element method was much less,but the pressure between the rigid finite element actually didn＇t exist and the tension within net line was ignored. These two weaknesses contributed mostly to the difference between simulation results and actual fish nets. Rigid finite element method may be suitable for some studies that need to get a rough net shape. Flexible finite element method overcame the two weaknesses of the rigid finite element method. Especially the adoption of lumped mass method and mass-spring system,the results of simulation using flexible finite element method were more realistic. And also this method increased the stability of numerical calculation process. The simulation results fit better with the experimental results（ Fig. 8,9）.Result suggest that： modeling of rigid finite element method has the advantage of simplifying model and can basically reflect the rough shape of nets. And with mesh line tension being ignored,the weakness is that it can not accurately reflect tension distribution and netting dynamics; flexible finite element method,based on the mass-spring system and Newton mechanical model,is majority,and the numerical simulation results fit better with the actual situation of fishing nets,and more realistic in net shape,and also the results of calculation and experimental results fit well; explicit algorithm is very sensitive to time step length,its stability and precision is no better than implicit algorithm. NEWTON-RAPHSON and NEWMARK-β algorithms have unconditional stability and convergence,and most studies choose them in model calculations.
出处
《海洋渔业》
CSCD
北大核心
2015年第3期277-287,共11页
Marine Fisheries
基金
国家863高技术研究发展计划(2012AA092301
2012AA092302
2012AA092303)
国家科技支撑计划(2013BAD13B05)
