Mathematical modeling of gas flow in plasma torch vortex chamber

Mathematical model of moving gas in vortex chamber (inter-electrode gas supply insert) of plasma torch channel was developed. Effect of moving electric arc on the motion of gas is considered. Software for solving problems of three dimensional non-ideal gas dynamics in complex areas was developed.Побудовано математичну модель руху газу у форсунці (міжелектродній вставці) і в області анода каналу плазматрона. Модель враховує вплив електричної дуги на течію газу. Розроблено програмний комплекс для рішення завдань тривимірної неідеальної газової динаміки в областях складної геометричної форми.Построена математическая модель движения газа в форсунке (межэлектродной вставке) и в области анода канала плазматрона. Модель учитывает влияние электрической дуги на течение газа. Разработан программный комплекс для решения задач трехмерной неидеальной газовой динамики в областях сложной геометрической формы

Development of exponential integrator based on classical Runge—Kutta method and it's application for solving stiff systems

Abstract: The paper deals with numerical method for solving stiff systems of ordinary differential equations. The new method RK4exp is derived on the base of classical four-stage Runge—Kutta method. The convergence of RK4exp is proved and it's stability function is calculated. Theoretical results are verified with numerical experiments.Note: Research direction:Mathematical problems and theory of numerical method

Development and application of numerical methods for solving tasks in unlimited regions based on the third Green formula

Abstract: The two-step algorithm for solving problems with a linear elliptic operator, for which the fundamental solution is known, is analyzed. New methods for solving problems in an unbounded areas with a mixed type operator are proposed: a method for expanding a domain, a method for specifying of integral boundary conditions and a three-step iterative method. The range of applicability of the constructed methods is limited by cases where outside a certain finite area the operators have a known fundamental solution and their right-hand side is homogeneous. To solve specific problems on the basis of the proposed methods, computational algorithms have been created, implemented in the form of computer software. A series of computational experiments confirming the correctness of the methods carried out. The results of calculations of the electromagnetic field around the rails of an electrodynamic rail-type accelerator in the two-dimensional case are presented.Note: Research direction:Mathematical modelling in actual problems of science and technic

Comparison of different mathematical and numerical models for cylindrical liner motion and their check

Abstract: The cylindrical liner motion at the action of electromagnetic forces is discussed. A set of calculations was carried out for modeling the motion of liner central part (without the influence of the supports). Another series of calculations was carried out for modeling the liner motion near the supports. The comparison of integral characteristics and liner profiles for elasto-plastic model and incompressible liquid model was executed. The influence of deformation curves and values of dynamic viscosity coefficient for liner motion characteristics was investigated. Results of a full-scale experiment on compression of a long thin-walled the liner with a diameter of 90 mm with pulse 6 MA current were shown.Note: Research direction:Mathematical modelling in actual problems of science and technic

Numerical solution of the dynamic contact problem of elasto-plastic bodies

Abstract: A plane dynamic problem of solid mechanics is considered. Basic relations for elastic and elasto-plastic materials are given. A finite element method for numerical solution of the problem is described, various time discretization schemes are presented. The dynamic contact problem formulation is given, a version of the Schwarz iterative method is proposed for its solution. The results of numerical solution for three test contact problems are shown: the problem of collision of two elastic rods and the problems of contact between two pipes in elastic and elastoplastic formulations (for the cross section). The convergence of the used Schwarz method is demonstrated on an example of calculation on refining grids.Note: Research direction:Mathematical modelling in actual problems of science and technic

Application of the Temetos software platform to electromagnetic accelerator simulation environment development

Abstract: The advance in the architecture of software platform Temetos for computing experiment supply is presented. The basic module of the platform and the system of subject libraries are described. The main principles of the platform development providing its painless growth and flexibility in adapting to various problems of mathematical modeling are presented. The experience of using the platform to develope a software environment for simulating an electromagnetic accelerator is described. An example of a calculation prepared using the developed software environment is given.Note: Research direction:Mathematical modelling in actual problems of science and technic