МАТЕМАТИЧЕСКОЕ ОПИСАНИЕ РАСПОРНОЙ ТРАЛОВОЙ ДОСКИ ДЛЯ ЗАДАЧ ЧИСЛЕННОГО МОДЕЛИРОВАНИЯ ДИНАМИКИ РАЗНОГЛУБИННЫХ ТРАЛОВЫХ СИСТЕМ

Abstract

A mathematical description of the spacer trawl doors of mid-water trawl system for numerical modeling by point mass method using a parallel architecture of a graphics processor is proposed, based on the representation of the dependence of the power characteristics of the door on its spatial and kinematic characteristics in tabular form. The construction of the tables is performed using the splitting method. To simulate the dynamics of a shallow mid-water trawl system using the point mass method, it is necessary to know all the masses concentrated at the nodes, the dependence of the distances between the nodes on the internal forces and the values of the external forces applied to the nodes (hydrostatic, hydrodynamic, trawler pulling forces). For a cable-net part of a trawl, a link is a section of a rope, a rope, a string or a rope, and a knot is the place of their connection. For the introduction of a trawl door into a general simulation model, it must be presented in the form of nodes and links. To simulate the influence of the trawl door on the dynamics of the entire mid-water trawl system over the velocity field using the Navier-Stokes equations systems, the pressure field is calculated by the numerical splitting method. Because of the great complexity of the splitting method, its application to calculate external forces at each iteration of the point mass algorithm on a personal computer in real time is not possible. Therefore, a faster method based on the composition of the cleavage methods for trawl doors and point masses for the cable-net part of the mid-water trawl system using tabular transformations and linear interpolation of intermediate values is proposed. For each type of trawl door, splitting simulation is performed for all possible combinations of linear and angular velocities with a given sampling rate, which is determined by comparing it with the available data based on the required accuracy. The results of each step compute the pressure field, and then the external forces applied to the nodes of the door. As a result, a six-dimensional table is obtained, which puts the external forces into correspondence with the velocities. To describe the construction of the trawl door, a piecewise linear approximation of the profile of all its elements (wing, slats) in the transverse plane of the section with a given degree of sampling, determined experimentally with allowance for a given error in calculations, is proposed. Such a model is acceptable for describing the majority of mid-water trawl doors used.