NUMERICAL ALGORITHM OF COMPUTATIONAL EXPERIMENT OF THE APPLIED OPTIMAL CONTROL PROBLEM IN SYSTEMS WITH DISTRIBUTED PARAMETERS

Stages of computing experiment of the developed algorithm by means of the final and differential scheme for the solution of applied problems of optimum control of the processes described by the solutions of elliptic type are given n article.

The main regularities of hydrodynamic effect caused by natural marine conditions on the underwater objects

Обеспечение управляемости морских объектов серьезно усложняется при их движении в сложных условиях морского волнения, ветра и других. Для подводных объектов важным фактором, влияющим на их движение, является существенная пространственно-временная неоднородность натурных гидрофизических полей плотности и скорости, а также внутренние волны, возникающие на границах резкого изменения плотности морской воды (пикноклина). Для проектирования и безопасного маневрирования в таких условиях необходимо знание основных закономерностей их воздействия на гидродинамику этих объектов. Использование натурного и модельного физического эксперимента для решения этой проблемы затрудняется ограниченными возможностями моделирования натурных условий, проблемой измерения нестационарных сил и моментов, а также наличием масштабного эффекта по критерию Рейнольдса. Наиболее эффективным способом решения задачи является применение методов вычислительной гидродинамики и компьютерных технологий. В статье излагаются результаты вычислительного эксперимента, проведенного на основе разработанных авторами физико-математической модели и численного метода прогнозирования силового воздействия морской среды на подводные объекты. Допущение о потенциальном характере течения согласуется с современными моделями как поверхностных, так и внутренних волн, и позволяет создать единую потенциальную гидродинамическую модель обтекания подводного объекта неоднородным потоком. При этом производится косвенный учет влияния вязкости на распределение давлений на корпусе путем введения специальной вихревой системы. В качестве модели внутренней волны используется модифицированная авторами двухслойная потенциальная модель Сретенского Л.Н. На основе анализа вычислительного эксперимента сформулирован ряд новых закономерностей такого воздействия, в частности, получены качественные и количественные зависимости гидродинамических сил от параметров пикноклина и внутренней волны, кораблестроительных характеристик объекта и ряда других. Предложенный программный продукт и выявленные закономерности могут быть использованы в практике проектирования подводных объектов, эксплуатируемых в условиях пространственно-временной неоднородности гидрофизических полей Океана и при создании тренажеров-имитаторов динамики морских объектов. Ensuring the controllability of marine objects is made much more difficult when they move in complex conditions of sea waves, wind and so forth. For underwater objects an important factor affecting their movement is a substantial spatio-temporal heterogeneity of natural hydrophysical fields of density and velocity, as well as internal waves that appear at the borderlines of a rapid change of sea water density (pycnocline). For designing and safe manoeuvring in such conditions it is necessary to know the main regularities of their effect on the hydrodynamics of these objects. Using a natural and model physical experiment to solve this problem is made harder by the limited capabilities of natural conditions modeling, the problem of measurement of unsteady forces and moments, as well as existence of a scale effect according to Reynolds criterion. The most efficient method to solve this task is application of methods of computational fluid dynamics and computer technology. The article presents the results of a computing experiment, which was conducted on the basis of a physico-mathematical model and numerical method for predicting a force impact of marine environment on the underwater objects. An assumption about a potential nature of the current is in agreement with the modern models of surface and internal waves, and this allows to create a unified potential hydrodynamical model of heterogeneity stream flowing around an underwater object. At the same time we make a indirect accounting for the effect of viscosity on pressure distribution on the hull by introducing a special vortex system. As a model for a internal wave we use a two layer potential model by L.N. Sretensky, modified by the authors. On the basis of analysis of the computing experiment several new regularities of such effect were formulated, in particular, as the result of experiment were obtained qualitative and quantitative relationships of hydrodynamic forces with pycnocline parameters and internal wave, shipbuilding characteristics of the object and some others. The proposed software product and the revealed regularities can be used in the practice of designing underwater objects operated in the conditions of spatio-temporal heterogeneity of the hydrophysical fields of the Ocean and in creating simulators for the dynamics of marine objects.

About calculation with the high accuracy of eigenvalues of the operator Laplace in the ellipse (with the regional condition of Neumann)

The method of the computing experiment investigates the task about fluctuations of the elliptic membrane with the regional condition of Neumann. It is shown that on the grid 40×61 it is possible to define up to 50 eigenvalues with several right significant figures for eccentricity e = 0.99999.

Determination of parameters of non-uniform fractured rock massif in computing experiment

The purpose of work is creation of the computing model that based on qualifiers of described elements of geomechanical system that having the nonlinear physical nature. The procedure of computing experiment conducting that based on application of net numerical methods with determination of admissible precision limit is developed for various description schemes of mechanical condition of the environment. The iterative computing experiment under control of the system of the external estimated indicators that defining structure and a format of the description of computing area of finite element method during rock massif modeling is conducted. The area of admissible values of parameters of the elements description of geomechanical system during solution of multiple parameter problem of optimization for implicitly set entry conditions is determined. Application limits in computing models of the following groups of characteristics of description elements of computing model are defined: macro -, mini- and mixed. The three-level system of the description of mechanical characteristics of geotechnical system that managing of multiple parameter network of qualifiers of the elements description of computing area is received. Parameters of calculations of contact tasks in difficult structured geomechanical models are qualitatively improved that is provided by increasing in accuracy of the description of geotechnical system elements. Accounting of nonlinear characteristics allows performing optimization of schemes of bolting systems for various mine conditions that based on a computing experiment. The presented studies were carried out on example of conditions of the «Almaznaya” mine, southern conveyor drift, coal seam l1, depth 550m. As a result, preservation of operational characteristics of extraction mine workings of Western Donbas that were drived in complicated mining-and-geological conditions is reached by the choice of optimum parameters of bolting systems that allowing to minimize production expenses. Results that based on the executed computing experiments using the considered procedure allowed to keep operational characteristics of extraction workings with economy of materials and labor costs at the level of 9 – 17%.