Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia2613610.22363/2658-4670-2021-29-1-5-13Research 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[S. L. Sobolev, “Local non-equilibrium transport models,” Physics Uspekhi, vol. 40, no. 10, pp. 1043-1053, 1997, in Russian. DOI: 10.1070/ PU1997v040n10ABEH000292.][S. I. Anisimov and B. S. Luk’yanchuk, “Selected problems of laser ablation theory,” Usp. Fiz. Nauk, vol. 172, no. 3, pp. 301-333, 2002. DOI: 10.3367/UFNr.0172.200203b.0301.][V. P. Veiko, M. N. Libensonm, G. G. Chervyakov, and E. B. Yakovlev, Interaction of laser radiation with matter. Power optics [Vzaimodeystviye lazernogo izlucheniya s veshchestvom. Silovaya optika], V. I. Konov, Ed. Moscow: Fizmatlit, 2008, in Russian.][M. P. Allen and D. J. Tildesley, Computer simulation of liquids. Clarendon Press, 1991.][Z. H. Jin, P. Gumbsch, K. Lu, and E. Ma, “Melting mechanisms at the limit of superheating,” Physical Review Letters, vol. 87, p. 055 703, 5 Jul. 2001. DOI: 10.1103/PhysRevLett.87.055703.][F. F. Abraham and J. Q. Broughton, “Pulsed melting of silicon (111) and (100) surfaces simulated by molecular dynamics,” Phys. Rev. Lett., vol. 56, pp. 734-737, 7 Feb. 1986. DOI: 10.1103/PhysRevLett.56.734.][V. Zhigilei and B. J. Garrison, “Pressure Waves in Microscopic Simulations of Laser Ablation,” in Materials Research Society (MRS) Proceedings, vol. 538, Cambridge University Press, 1998, pp. 491-496. DOI: 10.1557/ PROC-538-491.][J. I. Etcheverry and M. Mesaros, “Molecular dynamics simulation of the production of acoustic waves by pulsed laser irradiation,” Phys. Rev. B, vol. 60, pp. 9430-9434, 13 Oct. 1999. DOI: 10.1103/PhysRevB.60.9430.][L. V. Zhigilei and B. J. Garrison, “Microscopic mechanisms of laser ablation of organic solids in the thermal and stress confinement irradiation regimes,” Journal of Applied Physics, vol. 88, no. 3, pp. 1281-1298, 2000. DOI: 10.1063/1.373816.][A. V. Lykov, Heat and Mass Transfer [Teplomassoobmen], 2nd. Moscow: Energiya, 1978, in Russian.][P. Vernott, “Les paradoxes de la théorie continue de l’équation de la chaleur,” Comptes rendus de l’Académie des Sciences, vol. 246, no. 22, pp. 3154-3155, 1958.][E. M. Kartashov and V. A. Kudinov, Analytical methods of the theory of heat conduction and its applications [Analiticheskiye metody teorii teploprovodnosti i yeye prilozheniy]. Moscow: LENAND, 2018.][V. B. Fokin, “Continuous-automaton model and its application for numerical calculation of the effect of single and double femtosecond laser pulses on metals [Kontinual’no-atomaticheskaya model’ i yeye primeneniye dlya chislennogo rascheta vozdeystviya odinochnogo i dvoynogo femtosekundnogo lazernogo impul’sa na metally],” in Russian, Candidate of Sci. in Phys. and Math. (PhD) Thesis, Joint Institute for High Temperatures of the Russian Academy of Sciences, Moscow, 2017.]