Математическое моделирование UDC 519.633.6, 519.688 Numerical Algorithm for Simulation of Thermal Processes in Four Layer Cylindrical Object A. S. Ayriyan∗, J. Pribiˇ sice 9, Letn´ a, Koˇ s† ∗ Laboratory of Information Technologies Joint Institute for Nuclear Research 6, Joliot-Curie, Dubna, Moscow region, Russia, 141980 † Technical University in Koˇ sice, Slovak Republic, 04001 In the paper the algorithm is proposed for the numerical simulation of the thermal conductivity for the design and optimization of cryogenic cells pulsed (in the millisecond range) feeding the working gases into the electron-stringed source of multiply charged ions. <...> A model of the cryogenic cell with four layers (materials) is investigated. <...> The heat transfer into the object is described by the system of heat equations with temperature dependent discontinuous thermal coefficients. <...> The discontinuous thermal coefficients are given by experimental data and approximated by the least-squares method using the polynomial analytical functions. <...> The parallel algorithm for modeling thermal processes into four layer model was developed and speedup of the algorithm in depending on number of CPUs is shown. <...> Key words and phrases: heat transfer, explicit finite difference scheme, non-uniform grid, parallel algorithm, discontinuous thermal coefficients. 1. <...> Introduction The object shown in Fig. 1 is considered to be a cryogenic cell pulsed (millisecond range) feeding the working gases into the electron-string source of highly charged ions [1]. <...> The heat conductivity modeling in the composite object, when the object is heated by the electric current passing through one of the layer (graphite) is complex, especially if one of the layers is from 50 up to 1200 times less then the other ones. <...> The main goal of this work is implementation a model of thermal processes for a given object for systematic studies. 3 1 2 r 0 z Figure 1. <...> Equations and Boundary Conditions partial differential equations with temperature dependent discontinuous thermal coefficients [4]: ρmCV m(T)∂T ∂t = 1 ∂ ( r ∂r rλm(T)∂T ∂r ) + ∂ ∂z ( λm(T)∂T ∂z ) +Xm(T), The heat transfer into the object can be described by the following system of (1) where r ∈ [0, rmax <...>