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)2613610.22363/2658-4670-2021-29-1-5-13ArticlesСтатьиResearch ArticleNumerical simulation of thermal processes occurring in materials under the action of femtosecond laser pulsesЧисленное моделирование тепловых процессов, возникающих в материалах при воздействии фемтосекундных лазерных импульсовAmirkhanovIlkizar V.АмирхановИ. В.

Candidate of Physical and Mathematical Sciences, Head of Sector “Scientific Division of Computational Physics”

camir@jinr.ruSarkerNil R.СаркерН. Р.

Candidate of Physical and Mathematical Sciences, Senior Researcher “Scientific Division of Computational Physics”

sarker@jinr.ruSarkhadovIbrohimСархадовИ.

Candidate of Physical and Mathematical Sciences, Senior Researcher “Scientific Division of Computational Physics”

ibrohim@jinr.ruLaboratory of Information Technologies Joint Institute for Nuclear ResearchЛаборатория информационных технологий Объединенный институт ядерных исследований30032021291VOL 29, NO1 (2021)ТОМ 29, №1 (2021)51330032021Copyright ©; 2021, Amirkhanov I.V., Sarker N.R., Sarkhadov I.Copyright ©; 2021, Амирханов И.В., Саркер Н.Р., Сархадов И.2021Amirkhanov I.V., Sarker N.R., Sarkhadov I.Амирханов И.В., Саркер Н.Р., Сархадов И.http://creativecommons.org/licenses/by/4.0https://journals.rudn.ru/miph/article/view/26136

In this work, a numerical study of the solutions of the parabolic and hyperbolic equations of heat conduction with the same physical parameters is carried out and a comparative analysis of the results obtained is carried out. The mathematical formulation of the problem is discussed. The action of the laser is taken into account through the source function, which was chosen as a double femtosecond laser pulse. In the hyperbolic equation, in contrast to the parabolic one, there is an additional parameter that characterizes the relaxation time of the heat flux. In addition, the source of the hyperbolic equation contains an additional term - the derivative of the power density of the source of the parabolic equation. This means that the temperature of the sample is influenced not only by the power density of the source, but also by the rate of its change. The profiles of the sample temperature at different times and its dynamics at different target depths are shown. The calculations were carried out for different time delays between pulses and for different relaxation parameters.

В работе проведено численное исследование решений параболического и гиперболического уравнений теплопроводности при одинаковых физических параметрах, а также сравнительный анализ полученных результатов. Обсуждена математическая постановка задачи. Действие лазера учтено через функцию источника, которую выбрали в виде двойного фемтосекундного лазерного импульса. В гиперболическом уравнении, в отличие от параболического, присутствует дополнительный параметр, который характеризует время релаксации потока тепла. Кроме этого, в источнике гиперболического уравнения присутствует дополнительное слагаемое - производная от плотности мощности источника параболического уравнения. Это означает, что на температуру образца оказывает влияние не только плотность мощности источника, но и скорости его изменения. Приведены профили температуры образца в разные моменты времени и её динамика на разных глубинах мишени. Расчёты проводились при различных временах задержки между импульсами и при различных параметрах релаксации.

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