Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)2219310.22363/2658-4670-2019-27-1-21-32Computational modeling and simulationЧисленное и имитационное моделированиеResearch ArticleParallel algorithm for numerical solution of heat equation in complex cylindrical domainПараллельный алгоритм численного решения уравнения теплопроводности в сложной цилиндрической областиAyriyanAlexander SАйриянАлександр Сержикович

researcher of the Laboratory of Information Technologies

ayriyan@jinr.ruBuša JrJánБушаЯн мл.

PhD in Mathematics, Senior Researcher of the Laboratory of Information Technologies

busa@jinr.ruJoint Institute for Nuclear ResearchОбъединенный институт ядерных исследованийInstitute of Experimental Physics, Slovak Academy of SciencesИнститут экспериментальной физики Словацкой академии наук15122019271VOL 27, NO1 (2019)ТОМ 27, №1 (2019)213220112019Copyright ©; 2019, Ayriyan A.S., Buša Jr J.Copyright ©; 2019, Ayriyan A.S., Buša Jr J.2019Ayriyan A.S., Buša Jr J.Ayriyan A.S., Buša Jr J.http://creativecommons.org/licenses/by/4.0https://journals.rudn.ru/miph/article/view/22193

In this article we present a parallel algorithm for simulation of the heat conduction process inside the so-called pulse cryogenic cell. This simulation is important for designing the device for portion injection of working gases into ionization chamber of ion source. The simulation is based on the numerical solving of the quasilinear heat equation with periodic source in a multilayered cylindrical domain. For numerical solution the Alternating Direction Implicit (ADI) method is used. Due to the non-linearity of the heat equation the simple-iteration method has been applied. In order to ensure convergence of the iteration process, the adaptive time-step has been implemented. The parallelization of the calculation has been realized with shared memory application programming interface OpenMP and the performance of the parallel algorithm is in agreement with the case studies in literature.

В этой статье представлен параллельный алгоритм для моделирования процесса теплопроводности внутри, так называемой, импульсной криогенной ячейки. Это моделирование важно для разработки устройства для порционной подачи рабочих газов в ионизационную камеру источника ионов. Моделирование основано на численном решении квазилинейного уравнения теплопроводности с периодическим источником в многослойной цилиндрической области. Для численного решения используется метод неявного направления (ADI). Из-за нелинейности уравнения теплопроводности был применен метод простой итерации. Для обеспечения сходимости итерационного процесса был реализован адаптивный временной шаг. Распараллеливание вычислений было реализовано с помощью прикладного программного интерфейса с разделяемой памятью OpenMP, и производительность параллельного алгоритма согласуется с примерами из литературы.

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