An approach to numerical implementation of the diffusion-drift model is described with application to problem of estimating field effects induced in an object by a concentrated moving source. The mathematical model is formalized using initial boundary-value problem for multidimensional evolution equation of convection-reaction-diffusion type. The computational algorithm is based on modification of the predictor-corrector scheme intended for solving the diffusion problem and approximation of the drift component by the Roberts–Weiss scheme. The mathematical model has been implemented in the Matlab software package. The results of computing experiments attendant to variations of the control model parameters are presented.
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References
W. Hundsdorfer and J. G. Verwer, Numerical Solution of Time-Dependent Advection-Diffusion Reaction Equations Series, Springer, Berlin (2003).
D. Otten, Mathematical Models of Reaction Diffusion Systems, Their Numerical Solutions and the Freezing Method with Comsol Multiphysics, Bielefeld University Press, Bielefeld (2000).
J. B. Drake, Climate Modeling for Scientists and Engineers, University of Tennessee, Knoxville (2014).
G. I. Montecinos, Numerical methods for advection-diffusion-reaction equations and medical applications, PhD Thesis, University of Trento (2014).
X. Tan, e-Journal Prorab, No. 145, 1–24 (2013).
L. P. Kadanoff, Statistical Physics: Statics, Dynamics and Renormalization, World Scientific Publishing, London (2000).
S. V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation, Washington (1980).
A. A. Samarskii and P. N. Vabishchevich, Numerical Methods of Solving Convection-Diffusion Problems, Editorial URSS, Moscow (1999).
Y. E. Jin, J. Jiang, C. M. Hou, and D. H. Guan, J. Inform. Comput. Sci., 18, 5579–5586 (2012).
O. V. Shishkin, Sibirskii Matem. Zh., 48, No. 6, 1422–1428 (2007).
N. M. Afanas’eva, P. N. Vabishchevich, and M. V. Vasil’eva, Izv. Vyssh. Uchebn. Zaved. Matem., No. 3, 3–15 (2013).
L. A. Krukier, O. A. Pichugina, and B. L. Krukier, in: Proc. Int. Conf. Computational Science (ICCS), Vol. 18 (2013), pp. 2095–2100.
Z. Buckova, M. Ehrhardt, and M. Gunther, Alternating direction explicit methods for convection diffusion equations, Preprint Bergische Universitat Wuppertal Fachbereich Mathematik und Naturwissenschaften BUWIMACM 16/20 (2015), pp. 309–325.
J. Cazaux, Microsc. Microan., 10, No. 6, 670–680 (2004).
M. Kotera, K. Yamaguchi, and H. Suga, Jpn. J. Appl. Phys., 38, No. 12, 7176–7179 (1999).
B. Raftari, N. V. Budko, and C. Vuik, J. Appl. Phys., 118, 204101 (2015).
D. S. Chezganov, D. K. Kuznetsov, and V. Ya. Shur, Ferroelectrics, 496, 70–78 (2016).
A. Maslovskaya and A. Pavelchuk, Ferroelectrics, 476, 157–167 (2015).
A. V. Pavelchuk and A. G. Maslovskaya, in: Proc. IOP Conf. Series: J. Phys.: Conf. Series, 012009 (6 pp.) (2019).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 94–100, January, 2020.
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Pavelchuk, A.V., Maslovskaya, A.G. Approach to Numerical Implementation of the Drift-Diffusion Model of Field Effects Induced by a Moving Source. Russ Phys J 63, 105–112 (2020). https://doi.org/10.1007/s11182-020-02008-4
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DOI: https://doi.org/10.1007/s11182-020-02008-4