Wave propagation in two-species relativistic flows

Abstract

We consider system of hyperbolic balance laws governing relativistic two-fluid flow in which entropy is produced only by disequilibrium between the temperatures of the fluids. We compare two such models: one in which thermal equilibrium is attained through a relaxation procedure, and a fully relaxed model. We describe how the relaxation procedure may be made consistent with the second law of thermodynamics. The wave velocities for both models are obtained and compared: the mixture hydrodynamical velocity of the relaxed system is always less than the hydrodynamical velocity of the relaxation system.

Wave propagation in N-species relativistic flows

“…The relaxation procedure has been chosen to respect the second law of thermodynamics. In this respect, we have extended the results of a previous work [20], that considered the case of two fluids.…”

Diffuse interface method for two-species relativistic flows with heat transfer and particle interconversion

“…In this work, following the ideas of Saurel et al [11], Zein et al [17] and Flåtten et al [16,18], an extension of the results of previous work [30], in which only heat exchange is considered, is presented, including also the change of the number of particles of each species.…”

“…There are several approaches to multi-fluid flow processes in the classical [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and relativistic [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] contexts.…”

“…The paper is organized as follows. First of all, we present the basic relaxation model where heat transfer and particle interconversion between the components are modelled by relaxation source terms, taking as a starting point the model of work [30] in which the change of the number of particles of each species is not considered. We provide explicit expressions for these relaxation source terms that satisfy the second law of thermodynamics.…”

“…The starting point of the present analysis is the model proposed in [30], where there is no change of the number of particles:…”