Yu. G. Ispolov
Russia, 195251, St-Petersburg, Polytechnicheskaya st. 29
St.-Petersburg State Technical University
Department of Mechanics and control processes
E. A. Postoyalkina
Russia, 195251, St-Petersburg, Polytechnicheskaya st. 29
St.-Petersburg State Technical University
Department of Mechanics and control processes
N. N. Shabrov
Russia, 195251, St-Petersburg, Polytechnicheskaya st. 29
St.-Petersburg State Technical University
The problem of numerical solution of nonstationary heat conduction problem in a framework of finite element model is considered. New numerical methods of integration of differential equations of the problem are proposed. While elaboration of the methods the internal properties of the system that belongs to the systems having high energy dissipation, as well as the properties of finite element model of the system are taken into account. The three proposed methods belong to Runge-Kutta (RK) methods; the methods are of 3 stage, 3rd order and L-stable. The first and the second of the proposed methods are absolutely stable. The transition factor in RK methods is a ratio of two polynomials. The more is the difference of the polynomial powers in denominator and in numerator the better is the numerical reproduction of fast processes in the system, that is particularly important for stiff systems. In the transition factor of the first of the proposed method the difference of the polynomial powers is equal one. The first method is diagonally implicit that gives the opportunity to decrease computation time. The numerical scheme of the method includes the iterative process that has high convergence rate. In the transition factors of the second and the third of the proposed methods the differences of the polynomial powers are equal two and three respectively. These two methods are not diagonally implicit. The numerical schemes of the methods also include the iterative processes. The analysis of the iterative processes convergence was conducted and the algorithms that increase the convergence rate were proposed. The estimations of the influence of the coefficients of RK methods that determine the instants then the right parts of the equations are calculated on the accuracy of the methods were obtained. The quality of performance of the proposed methods was checked on several test problems. The industrial problem of the computation of nonstationary temperature field in power steam turbine rotor was solved. Numerical experiments confirm the high accuracy of the solution and decrease of computation time in comparison with generally used methods.