Discrete 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)2613610.22363/2658-4670-2021-29-1-5-13Research ArticleNumerical simulation of thermal processes occurring in materials under the action of femtosecond laser pulsesAmirkhanovIlkizar V.<p>Candidate of Physical and Mathematical Sciences, Head of Sector “Scientific Division of Computational Physics”</p>camir@jinr.ruSarkerNil R.<p>Candidate of Physical and Mathematical Sciences, Senior Researcher “Scientific Division of Computational Physics”</p>sarker@jinr.ruSarkhadovIbrohim<p>Candidate of Physical and Mathematical Sciences, Senior Researcher “Scientific Division of Computational Physics”</p>ibrohim@jinr.ruLaboratory of Information Technologies Joint Institute for Nuclear Research3003202129151330032021Copyright © 2021, Amirkhanov I.V., Sarker N.R., Sarkhadov I.2021<p style="text-align: justify;">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.</p>parabolic and hyperbolic heat equationsfemtosecond laser pulsenumerical simulationпараболическое и гиперболическое уравнения теплопроводностифемтосекундный лазерный импульсчисленное моделирование<p>Introduction The study of the interaction of femtosecond laser pulses with matter is important in connection with many fundamental problems (physics of non- equilibrium processes, generation of shock waves, laser acceleration of ions, modification of the properties of the irradiated material, etc.) [1]-[3]. Currently, there is a growing need for the creation and improvement of physical models capable of describing various processes in matter. Moreover, computer modeling now occupies one of the main places in the study of such problems. There are two approaches to the study and creation of physical models - atomistic and continuous. Atomistic approaches (molecular dynamics method) allow natural consider- ation of the atomic structure of the crystal lattice, the effect of impurities, the presence of dislocations, the kinetics of phase transitions, etc. The contin- ual approach (solving the equations of continuum mechanics) includes the parabolic and hyperbolic heat equation, the two-temperature model of heat conduction, the two-temperature hydrodynamic model, etc. [2]. The molecular dynamics (MD) method [4] can be used to describe the dynamics of fast processes that arise in a substance under the action of a laser pulse. MD is quite effective for microscopic analysis of the mechanisms of melting and evaporation [5], [6]. The appearance and propagation of pressure waves generated by laser radiation [7], [8], as well as the dynamics of laser ablation [9], are well modeled using the MD. Each approach has its own problems. When studying transport processes within the framework of a parabolic equation, a problem that arises is the infinitely high speed of thermal perturbation propagation (a consequence of the Fourier law). Generalizing the Fourier law, taking into account the relaxation time of the heat flux, we obtain the hyperbolic equation of heat conduction. The relaxation time is a characteristic of nonequilibrium of the heat conduction process. Under exposure to femtosecond pulses, non-equilibrium heating of the material occurs. Therefore, the study of such processes may turn out to be more adequate using the hyperbolic heat equation. In this work, we carried out a numerical study of the physical processes arising under the action of femtosecond laser pulses within the framework of the parabolic and hyperbolic equations of heat conduction and carried out a comparative analysis of the results obtained. 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