Verification of the Wave Factorization Method for Calculation of Distributed Systems During Towing in a Flow in Acceleration Mode

Abstract

For purposes of asymmetric confrontation with the Russian Navy, distributed systems (DS; cable, tethered, etc.) for unmanned underwater vehicles need further development and improvement. To date, specifics and methods of designing such DSs are insufficiently covered in scientific and technical literature. Distributed systems include towed systems of constant or variable length in a flow of liquid, underwater communication cables, pillars of offshore oil platforms, etc. This definition includes mechanical objects with one of the linear dimensions at least 10 – 20 times larger than the other two. The main limitations for application of the finite difference method (FDM) for numerical modeling of wave propagation and reflection in DS are the peculiarities of the defining quasi-linear equations. They are related to the need of simultaneous calculation of variables responsible for fast and slow wave processes. The term "singularly perturbed system of equations" is used for such systems of equations. These perturbations are the result of a significant difference in propagation velocities of longitudinal, configurational, bending, and torsional waves in DS at the physical level, etc. In this regard, it is necessary to apply the special step-by-step methods of regularization and filtering of numerical results. This imposes certain limitations on the possibility of simulating real processes and on the accuracy of obtained results, and forces the use of the implicit difference schemes and high-frequency filtering. The method of parallelization of the finite-difference operator and the program code according to the wave type is considered. The idea of parallelization by waves is based on the physical feature of propagation of different types of waves in distributed systems – a difference of 10 – 100 or more times between the propagation velocities of the longitudinal, transverse (configurational), bending and torsional waves in DS. The increase in productivity of the MPI version of a programming code when performing calculations on the SMP system is on average at least 30 – 100%, depending on the required accuracy of calculations and parallelization options. The version of the parallelized code, which uses the wave factorization method, is relevant when solving tasks of DS control, operational numerical analysis of transient modes of motion, etc., where performance is critically necessary. The comparative assessment of the accuracy of the experimental data, the original (non-parallelized) algorithm and the parallelized algorithm was carried out using the example of the numerical solution of the problem of the towing vessel’s movement in the acceleration mode when towing the DS.