An 18 Moments Model for Dense Gases: Entropy and Galilean Relativity Principles without Expansions

Abstract

The 14 moments model for dense gases, introduced in the last few years by Arima, Taniguchi, Ruggeri and Sugiyama, is here extended up to 18 moments. They have found the closure of the balance equations up to a finite order with respect to equilibrium; it is also possible to impose for that model the entropy and Galilean relativity principles up to whatever order with respect to equilibrium, but by using Taylor's expansion. Here, the exact solution is found, without expansions, but a bigger number of moments has to be considered and reasons will be shown suggesting that this number is at least 18.

Extended Thermodynamics for Dense Gases up to Whatever Order and with Only Some Symmetries

“…We firstly note that the second term in Equation (39) is zero thanks to Equation (33). We can take the derivative with respect to λ of what remains and substitute Equation (31).…”

“…A new approach has been proposed in [24] and other articles, such as [25][26][27][28][29][30][31][32][33][34][35][36][37][38], which overcomes this problem by considering two blocks of balance equations. In this framework, we have recently studied two different cases: one deals with rarefied polyatomic gases [37], even if the reduced set of applicability is not indicated in the title of that paper.…”

“…A natural way to impose this principle is described in [33] for the 18-moment model. It extends, to the two-block theory, the method described in [41] with the further deepening of [42] for the old one-block theory.…”

“…It extends, to the two-block theory, the method described in [41] with the further deepening of [42] for the old one-block theory. The resulting Equations (13) and (14) of [33] contain two additional variables with respect to the present model, that is µ ill and λ ll ; by making these variables equal to zero, we obtain the counterpart for our model, that is:…”

Relativistic extended thermodynamics from the Lagrangian view-point

“…They started a new framework of research where many and many other articles followed them. Some of them have been published in the last years and are [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”