Numerical simulation of hydrodynamics of an axisymmetric grid structure using the "vortex – current function" method

The article presents a mathematical and simulation model for modeling the hydrodynamics of axisymmetric mesh structures such as a trawl codend using the vortex–current function method. The novelty of the research is to reduce the problem to calculation in a two-dimensional coordinate system, which will reduce the complexity of calculations and speed up the process of obtaining a result. The advantages and disadvantages of the method are described. Systems of partial differential equations, as well as finite difference schemes and methods for their solution are presented. The initial and boundary conditions are indicated. Algorithms for solving the Navier-Stokes and Poisson equations for a heterogeneous computing system are proposed. An implicit finite-difference scheme and a solution by splitting methods to obtain tridiagonal systems of linear equations are considered. Their solution by the run-through method is shown. The result of numerical simulation using the ω–ψ method on the developed computer program is presented. The obtained results are compared with the results of numerical modeling based on heuristic dependencies. It is shown that the results of numerical simulation are consistent with the data of a field experiment in a hydraulic channel. Scope of application: scientific research, educational process, design and operation of fishing trawls, virtual reality systems.

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