The entropy of a thermodynamic graph

01/31/2018 ∙ by O. Kurganskyy, et al. ∙ GMX 0

We introduce an algorithmic model of heat conduction, the thermodynamic graph. The thermodynamic graph is analogous to meshes in the finite difference method in the sense that the calculation of temperature is carried out at the vertices of the graph, and the edges indicate the direct heat exchange between the vertices. Recurrence relations of heat conduction in graph are derived without using of differential equations and based on the coefficients of thermal conductivity and heat capacity. This approach seems to be more direct and flexible from the point of view of algorithmic modeling of thermodynamic process than the derivation of difference schemes from differential equations. We introduce also the notion of entropy of thermodynamic graph. We find the maximum length of the time step at which the entropy does not decrease in the general case. As a result, this give us the accurate boundary of the model stability.

READ FULL TEXT VIEW PDF
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.

Список литературы

  • [1]
  • [2] Ivanova A.A. Predictive Control of Water Discharge in the Secondary Cooling Zone of a Continuous Caster // Metallurgist. – 2013. – 57, issue 7–8. – P. 592–599. DOI: 10.1007/s11015-013-9775-0.
  • [3]
  • [4] Препарата Ф., Шеймос М. Вычислительная геометрия: Введение. – М.: Мир, 1989. – 295 c.
  • [5]
  • [6] Самарский А.А., Гулин А.В. Устойчивость разностных схем, – М.: Наука, 1973. – 415 с.
  • [7]
  • [8] Иванова А.А., Курганский А.Н. Математическое моделирование положения двухфазной зоны в непрерывнолитом слитке // XV Минский междунар. форум по тепломассообмену, Минск, 23–26 мая 2016. – С. 331–334.
  • [9]