Spectral methods for numerical simulation of high-energy particle interactions
Yazdani Hasanyazdani.hasan@niu.edu.inDepartment of Computer Sciences and EngineeringNoida International UniversityGreater Noida, Uttar Pradesh, 201312, IndiaView full profile → , *Suhas BhiseCorresponding authorsuhas.bhise@vit.eduDepartment of Electronics and Telecommunication EngineeringVishwakarma Institute of TechnologyPune, Maharashtra, 411037, IndiaView full profile → , Wamika Goyalwamika.goyal.orp@chitkara.edu.inCentre for Research Impact and Outcome (CRIO)Chitkara UniversityRajpura, Punjab, 140401, IndiaView full profile → , Chandra Sekhar Koppireddycskoppireddy@outlook.comDepartment of Computer Science & EngineeringPragati Engineering CollegeSurampalem, Andhra Pradesh, 533437, IndiaView full profile → , S. D. Ahmeduddinahmed1697@vardhaman.orgDepartment of Computer Science and EngineeringVardhaman College of EngineeringHyderabad, Telangana, 501218, IndiaView full profile → , Tirukoti Sudha Ranisudharani.tirukoti@adityauniversity.inDepartment of Computer Science and EngineeringAditya UniversitySurampalem, Andhra Pradesh, 533437, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Apr 2026
- Published Online:
- 27 Oct 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2813
- Pages:
- 2983–2994
Abstract
The high energy particle interactions are very complex phenomena, characterized by nonlinear, partial differential equations, and require very accurate numerical methods to simulate these phenomena reliably. The efficiency of the spectal methods in representing smooth solution fields, the superior accuracy and the exponential convergence make them very powerful computational tools. A comprehensive overview of the spectral techniques useful for numerical simulation of high energy particle interaction is presented; the Chebyshev and Legendre polynomial based methods are discussed in detail. The numerical stability and the computational efficiency are enhanced by introducing a nonlinear term evaluation, implementing boundary conditions, and physically consistent model parameters in the proposed framework. The validation of the simulation results is carried out for characteristics of the particle field evolution, dynamics of energy transport and interaction between particles, which reduces the discretization errors compared with the results of the use of conventional finite difference methods. The results validate the use of spectral methods in developing efficient, robust and scalable computational tools to study complex phenomena of high energy particles that are relevant to a broad spectrum of scientific and engineering applications.
Keywords
Subject Classifications
References
[1] C. C. Monsia, H. Zan, and H. Wen, "Numerical simulation and experimental study of influence particles on controlled vibration based on acoustic black hole," Applied Sciences, vol. 16, no. 5, Art. no. 2428 (2026), doi: 10.3390/app16052428.
[2] K. Volkov, "Numerical modeling of a gas–particle flow induced by the interaction of a shock wave with a cloud of particles," Mathematics, vol. 13, no. 21, Art. no. 3427 (2025), doi: 10.3390/math13213427.
[3] X. Du, Y. Shi, Q. Yang, D. Song, and X. Liu, "Numerical simulation of spectral radiation for hypersonic vehicles," Aerospace, vol. 11, no. 10, Art. no. 802 (2024), doi: 10.3390/aerospace11100802.
[4] Y. Wang and S. Markovych, "Technical analyses of particle impact simulation methods for modern and prospective coating spraying processes," Coatings, vol. 15, no. 12, Art. no. 1480 (2025), doi: 10.3390/coatings15121480.
[5] M. Tripathi, S. Dykas, M. Majkut, K. Smołka, K. Skoczylas, and A. Boguslawski, "Spectral energy of high-speed over-expanded nozzle flows at different pressure ratios," Energies, vol. 18, no. 21, Art. no. 5813 (2025), doi: 10.3390/en18215813.
[6] Y. Yao, Y. Zheng, and Y. Yang, "Numerical simulation of energy and mass transfer in a magnetic stirring photocatalytic reactor," Sustainability, vol. 15, no. 9, Art. no. 7604 (2023), doi: 10.3390/su15097604.
[7] P. B. Ryzhakov, J. Marti, and M. R. Hashemi, "Advances in numerical modeling of coupled CFD problems," Journal of Marine Science and Engineering, vol. 11, no. 5, Art. no. 978 (2023), doi: 10.3390/jmse11050978.
[8] M. A. R. Sheikh, X. Liu, T. Matsumoto, K. Morita, L. Guo, T. Suzuki, and K. Kamiyama, "Numerical simulation of the solid particle sedimentation and bed formation behaviors using a hybrid method," Energies, vol. 13, no. 19, Art. no. 5018 (2020), doi: 10.3390/en13195018.
[9] E. Sebastian and R. C. Poonia, “Entropy diagnostics for cryptographic key material from random circuit sampling,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 29, no. 2-B, pp. 1023–1032 (2026), doi: 10.47974/JDMSC-2641.
[10] R. A. Obaid, M. A. Kadhim, and A. M. Abed, "A comparative study of approximate solutions to solving second-order linear complex partial differential equations," Journal of Interdisciplinary Mathematics, vol. 29, no. 5-B, pp. 1475–1486 (2026), doi: 10.47974/JIM-2535.
[11] Z. Ba and Y. Wang, "Numerical analysis of transient state heat transfer by spectral method based on POD reduced-order extrapolation algorithm," Applied Sciences, vol. 13, no. 11, Art. no. 6665 (2023), doi: 10.3390/app13116665.
[12] Y. Jia, D. Wang, and X. Guo, "High-dimensional numerical methods for nonlocal models," Mathematics, vol. 13, no. 21, Art. no. 3512 (2025), doi: 10.3390/math13213512.
[13] Y. Rodimkov, E. Efimenko, V. Volokitin, E. Panova, A. Polovinkin, I. Meyerov, and A. Gonoskov, "ML-based analysis of particle distributions in high-intensity laser experiments: Role of binning strategy," Entropy, vol. 23, no. 1, Art. no. 21 (2021), doi: 10.3390/e23010021.
[14] S. Guerdouh and W. Chikouche, "A full Nesterov-Todd step feasible interior-point algorithm for semidefinite optimization based on a new hyperbolic barrier function," Journal of Information and Optimization Sciences, vol. 47, no. 4, pp. 1359–1376 (2026), doi: 10.47974/JIOS-1604.
[15] E. Fazlioglu, "Adaptive scheduling framework for distributed renewable energy systems," International Journal on Advanced Computer Theory and Engineering, vol. 15, no. 2, pp. 87–92 (2026), doi: 10.65521/ijacte.v15i2.3323.
