Causal viscous hydrodynamics -- the different 2nd order formalisms

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Israel-Stewart (I-S) Formalism[1,2,3]:

(used by codes from Song&Heinz (VISH2+1,OSU)[4,5], Romatsche&Romatschke (INT)[6], Huovinen&Molnar(Purdue)[7], Chaudhuri(Calcutta)[8])

* Simplified I-S formalism: (used by code from Song&Heinz[4] (VISH2+1,OSU))

  • (1) (--simplified I-S eqn )

* Full I-S formalism from conformal symmetry constraint: (used by code from Romatsche&Romatschke[6](INT))

  • (2) (--full I-S eqn-R&R)

* Full I-S formalism from 2nd law of thermodyamics: (used by code from Song&Heinz[5](VISH2+1,OSU))

  • (3) (--full I-S eqn-S&H)

Ottinger-Grmela (O-G) Formalism[9]:

(used by code from Dusling&Teaney(SUNY)[10])

In this pdf document we compare the equations for the OG and IS formalisms.

In summary the OG formalism yields:


For a conformal fluid one should choose

to do list:

[1] W. Israel, Ann. Phys. (NY) 100 (1976) 310; W. Israel and J. M. Stewart, Phys. Lett. 58A, 213 (1976); W. Israel and J. M. Stewart, Ann. Phys. (NY) 118 (1979) 341.
[2] A. Muronga and D. H. Rischke, arXiv:nucl-th/0407114.A. Muronga Phys. Rev. C 69, 034903 (2004); A. Muronga, Phys. Rev. C76 014909and 014910 (2007).
[3] U. W. Heinz, H. Song, A. K. Chaudhuri, Phys.Rev.C73:034904,2006.
[4] H. Song and U. Heinz, Phys.Lett.B 658, 279,(2008); Phys.Rev.C77, 064901, (2008).
[5] H. Song and U. Heinz, arXiv:0805.1756 (nucl-th), PRC in press.
[6] P. Romatschke and U. Romatschke, Phys.Rev.Lett.99, 172301 (2007). M. Luzum and P. Romatschke, arXiv:0804.4015 (nucl-th).
[7] D. Molnar, P. Huovinen, arXiv:0806.1367 (nucl-th).
[8] A. K. Chaudhuri,arXiv:0708.1752 (nucl-th); arXiv:0801.3180 (nucl-th) and arXiv:0803.0643 (nucl-th).
[9] M. Grmela, H. C. Ottinger, Phys. Rev. E 56, 6620 (1997); H. C. Ottinger, M. Grmela, Phys. Rev. E 56, 6633 (1997); H. C. Ottinger, Phys. Rev. E 57, 1416 (1998).
[10] K. Dusling, D. Teaney, Phys.Rev.C77:034905,2008.

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