Abstract—The paper is referring to distributed parameter propagation phenomena, in relation to the Cartesian coordinate axes (0p;0q;0r). The analogical model of the propagation phenomenon is expressed through a partial differential equation of second (II) order, associated to each coordinate axis. The numerical integration is based on the matrix of partial derivatives of the state vector (Mpdx), that uses approximating solutions for the calculations start. The numerical simulation of the propagation phenomenon follows parametrical spatial curves predetermined in relation to time (t), respectively p = p(t), q = q(t), and r = r(t), in the period t0 ≤ t ≤ tf . The examples run on the computer are referring to identical or different propagation parameters in relation to the three Cartesian coordinate axes. The numerical simulation evolves after spatial curves in form of a spiral, which encloses significantly the evolution of the studied phenomenon. Some references are made on the applicability of the elaborated programs, for chemical, metallurgical, pollution processes etc.
Index Terms—Partial differential equations (PDEs), analogical modeling, numerical simulation, matrix of partial derivatives of the state vector, thermal propagation, structure parameters, approximating solutions.
The authors are with the Politehnica University of Bucharest, Bucharest, Romania (e-mail: d_bes@yahoo.com, eddy_milan91@yahoo.com, octavdontu@yahoo.com, victor.f.constantin@gmail.com, spanu_alina@yahoo.com, robert.ciobanu185@yahoo.com).
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Cite: Vlad Mureşan, Iulia Clitan, Tiberiu Coloşi, Mihail Abrudean, Mihaela-Ligia Ungureşan, and Andrei Clitan, "Numerical Simulation on Spatial Curves for Distributed Parameter Propagation Processes," International Journal of Modeling and Optimization vol. 8, no. 4, pp. 202-207, 2018.
