Algorithm for finding parameters of equations of state based on the particle swarm optimization

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Resumo

The algorithm for finding the parameters of the equations of state is described. The proposed algorithm is based on the particle swarm optimization, which is applied to three simple models based on the van der Waals equation (in the form of pressure function upon specific volume and temperature) and two of its modifications.

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Sobre autores

K. Boyarskikh

Joint Institute for High Temperatures of the Russian Academy of Sciences; Moscow Institute of Physics and Technology

Autor responsável pela correspondência
Email: boyarskikh.ka@phystech.edu
Rússia, Moscow; Dolgoprudny

K. Khishchenko

Moscow Institute of Physics and Technology; South Ural State University; South Ural State University

Email: boyarskikh.ka@phystech.edu
Rússia, Moscow; Dolgoprudny; Chelyabinsk

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2. Fig. 1. Illustration of the algorithm operation based on the particle swarm method. The parameters of the M1 equation are plotted along the axes. The black circles show the position of the particles at t = 0, the red square – at t = 728 (the particles converged to one point with the required accuracy). The green cross determines the position of the global minimum of the functional at t = 728. This illustrates the fact that the optimum was reached during the algorithm operation.

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3. Fig. 2. The number of iterations NT (during the algorithm operation) and the achieved smallest deviation from the experimental data δρ (5) depending on the number of particles NI. The number of particles NI is plotted along the abscissa axis.

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4. Fig. 3. Shock adiabats (H1–H6) and unloading isentropes (S1 and S2) for tungsten samples with initial density ρ00 = 4.60 (H1), 5.50, 6.64, 8.87 (S1, S2), 10.59 and 13.36 g∙cm−3 ρ00 = 13.36 (H1), 10.59, 8.87 (S1, S2), 6.64, 5.50, and 4.60 g∙cm−3 (H6); Markers are experimental data (P0, P3, P5, P6, P9, K3 – [29]; P1, P5 – [30]; P2, P8, K2 – [28]; P7, K1 – [27]; R1, R2 – [31]), some of which (K1, K2, K3) fall outside the region V > b. Isentropes S1 and S2 correspond to the mass velocity on the shock adiabat U = 2.7 and 3.11 km∙s−1; purple, violet and light blue lines are the results of isentrope calculations using models M1, M2 and M3, respectively, taking into account the formation of a two-phase liquid–vapor mixture (solid lines) and metastable single-phase states (dashed lines).

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