Geodesic
Modeling wave processes by the particle dynamics method
Matematičeskoe modelirovanie, Tome 32 (2020) no. 10, pp. 119-134.

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We propose а method for the numerical simulation of acoustic processes, in solids representing a solid in the form of an array of particles in a cubic body-centered crystal lattice. Particle dynamics is described by Newton's equations of motion. It is shown that the developed numerical model allows one to describe resonance phenomena and the process of wave propagation. The results of modeling the resonant frequencies of an ultrasonic instrument by the proposed method and the finite element method in a COMSOL Multiphysics environment are compared. An experimental study of the resonant frequencies of an ultrasonic instrument showed that the numerical model correctly determines its resonant frequencies.
Keywords: acoustics, particle dynamics, Newton's law, COMSOL Multiphysics, cubic volume-centered crystal lattice, molecular dynamics method. 
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D. Ya. Sukhanov; A. E. Kuzovova. Modeling wave processes by the particle dynamics method. Matematičeskoe modelirovanie, Tome 32 (2020) no. 10, pp. 119-134. http://geodesic.mathdoc.fr/item/MM_2020_32_10_a8/

[1] S. L. Ilmenkov, A. A. Kleshchev, A. S. Klimenkov, “The Green's Function Method in the Problem of Sound Diffraction by an Elastic Shell of Noncanonical Shape”, Acoustical Physics, 60:6 (2014), 617–623 | DOI | DOI

[2] S. E. Kireev, “Parallelnaia realizatsiia metoda chastits v iacheikakh dlia modelirovaniia zadach gravitatsionnoi kosmodinamiki”, Avtometriia, 42:3 (2006), 32–39 | MR

[3] G. Riccardi, De Bernardis, “Numerical simulations of the dynamics and the acoustics of an axisymmetric bubble rising in an inviscid liquid”, European J. of Mechanics, B/Fluids, 2020, 121–140 | DOI | MR | Zbl

[4] T. Cavalieri, J. Boulvert, L. Schwan, G. Gabard, V. Romero-Garcìa, J. P. Groby, M. Escouflaire, J. Mardjono, “Acoustic wave propagation in effective graded fully anisotropic fluid layers”, J. of the Acoustical Society of America, 146:5 (2019), 3400–3408 | DOI | MR

[5] A. N. Tikhonov, A. A. Samarskii, Uravneniia matematicheskoi fiziki, Nauka, M., 1977 | MR

[6] B. Gilvey, J. Trevelyan, G. Hattori, “Singular enrichment functions for Helmholtz scattering at corner locations using the boundary element method”, Intern. J. for Numerical Methods in Eng., 121:3 (2020), 519–533 | DOI

[7] S. G. Golovina, E. V. Zakharov, “Chislennyi metod resheniia obratnoi zadachi dlia volnovogo uravneniia v srede s lokalnoi neodnorodnostiu”, Vestnik Moskovskogo Universiteta. Seriia 15. Vychislitelnaia matematika i kibernetika, 2017, no. 4, 22–27 | Zbl

[8] M. Takemura, M. Toyoda, “Analysis of the oblique incidence of periodic structures in a sound field by the finite-difference time-domain method”, Applied Acoustics, 167 (2020), 107357, 10 pp. | DOI

[9] V. A. Barkhatov, “Reshenie volnovykh uravnenii metodom konechnykh raznostei vo vremennoi oblasti. Dvumernaia zadacha. Osnovnye sootnosheniia”, Defektoskopiia, 2007, no. 9, 54–70

[10] D. A. Avdeev, V. I. Rimliand, “Trekhmernoe modelirovanie akusticheskogo polia metodom konechnykh raznostei vo vremennoi oblasti”, Vestnik TOGU, 2016

[11] ZH. O. Dombrovskaia, “Metod konechnykh raznostei vo vremennoi oblasti dlia kusocho-odnorodnykh dielektricheskikh sred”, Modelirovanie i analiz informatsionnykh system, 23:5 (2016), 539–547 | MR

[12] V. Jagota, A. Preet Singh Sethi, K. Kumar, “Finite Element Method: An Overview”, Walailak Journal. Sci. and Technology, 10:1 (2013), 1–8

[13] A. Di Vincenzo, M. Floriano, “Realistic Implementation of the Particle Model for the Visualization of Nanoparticle Precipitation and Growth”, J. of Chemical Educ., 96:8 (2019), 1654–1662 | DOI

[14] S. Hu, R. Fu, “Expanding the flexibility of dynamics simulation on different size particle-particle interactions by dielectrophoresis”, J. of Biological Physics, 45:1 (2019), 45–62 | DOI

[15] A. A. Selezenev, Osnovy metoda molekuliarnoi dinamiki, Uch. metod. pos., SarFTI, Sarov, 2017, 72 pp.

[16] S. S. Sharma, B. B. Sharma, A. Parashar, “Mechanical and fracture behavior of water submerged grapheme”, Journal of Applied Physics, 125:21 (2019), 1–8 | DOI

[17] V. D. Natsik, S. N. Smirnov, V. I. Belan, “Computer modeling and analytical description of structural defects in two-dimensional crystals of bounded sizes: Free boundary, dislocations, and crowdions”, Low Temperature Physics, 44:7 (2018), 688–695

[18] S. Starikov, V. Tseplyaev, “Two-scale simulation of plasticity in molybdenum: Combination of atomistic simulation and dislocation dynamics with non-linear mobility function”, Comp. Materials Sci., 179 (2020), 1–14

[19] B. Zhang, L. Zhou, Yu Sun, W. He, Y. Chen, “Molecular dynamics simulation of crack growth in pure titanium under uniaxial tension”, Molecular Simul., 44:15 (2018), 1252–1260 | DOI

[20] J. Li, B. Lu, H. Zhou, C. Tian, Y. Xian, G. Hu, R. Xia, “Molecular dynamics simulation of mechanical properties of nanocrystalline platinum: Grain-size and temperature effects”, Phys. Letters A, 383:16 (2019), 1922–1928 | DOI

[21] S. L. Duncan, I. S. Dalal, R. G. Larson, “Molecular dynamics simulation of phase transitions in model lung surfactant monolayers”, Biochimica et Biophysica Acta (BBA) Biomembranes, 1808:10 (2011), 2450–2465

[22] V. L. Kovalev, V. IU. Sazonova, A. N. IAkunchikov, “Modelirovanie vzaimodeistviia strui razrezhennogo gaza s pregradoi metodami molekuliarnoi dinamiki”, Vest. Mosk. universiteta. Ser. 1, Matematika, Mekhanika, 2008, no. 2, 56–58 | Zbl

[23] V. V. Zubkov, P. V. Komarov, “Izuchenie struktury ultratonkogo sloia dikhlormetana na ploskoi grafitovoi poverkhnosti metodami teorii funktsionala plotnosti I molekuliarnoi dinamiki”, Vest. Tverskogo gos. univ., ser.: KHimiia, 2010, no. 10, 37–46

[24] D. Y. Lenev, G. E. Norman, “Molecular Modeling of the Thermal Accommodation of Argon Atoms on Clusters of Iron Atoms”, High Temperature, 57:4 (2019), 490–497

[25] V. L. Malyshev, D. F. Marin, E. F. Moiseeva, N. A. Gumerov, I. SH. Akhatov, “Issledovanie prochnosti zhidkosti na razryv metodami molekuliarnoi dinamiki”, Teplofizika vysokikh temperatur, 53:3 (2015), 423

[26] V. A. Balashov, “Direct Simulation of Moderately Rarefied Gas Flows in Two-Dimensional Model Porous Media”, Math. Mod. and Comp. Simul., 10:4 (2018), 483–493 | MR

[27] S. Marburg, Six boundary elements per wavelength: Is that enough?, J. of Computational Acoustics, 10:1 (2002), 25–51 | DOI | MR

[28] V. M. Verzhbitskii, Osnovy chislennykh metodov, Uch. dlia vuzov, Vysshaia shkola, M., 2002, 840 pp.

[29] A. M. Krivtsov, Deformirovanie i razrushenie tverdykh tel s mikrostrukturoi, Fizmatlit, M., 2007, 304 pp.