Thermodynamics, Conservation Laws and their Rotation Invariance

  • S. K. Godunov

Abstract

Late in the 1950s, when I developed methods of gasdynamics computations, I, being under the influence of variational principles, arrive at a conclusion that the equations of gasdynamics belong to the class of equations of the following form:
$$ \frac{{\partial {L_{qi}}}}{{\partial t}} + \frac{{\partial M_{{q_i}}^j}}{{\partial {x_j}}} = 0. $$
(1)
On smooth solutions to these equations, one more additional relation holds:
$$ \frac{{\partial \left( {{q_i}{L_{qi}} - L} \right)}}{{\partial t}} + \frac{{\partial \left( {{q_i}M_{{q_i}}^j - {M^j}} \right)}}{{\partial {x_j}}} = 0. $$
(2)
In fact, this relation is a thermodynamic identity.

Keywords

Enthalpy Thermodynamics 

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References

  1. 1.
    Godunov S. K. (1960) On the concept of generalized solution. Soviet. Math. Dokl, Vol. 1, pp. 1194–1196, 1960.MathSciNetMATHGoogle Scholar
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    Godunov S. K. and Romenskii E. I. (1998) Elements of Continuous Media and Conservation Laws. Universitetskaya Seriya. Vol. 4. Scientific Books Publisher. Novosibirsk.1998 [in Russian].Google Scholar
  3. 3.
    Godunov S. K., Romenskii E. I., and Mihailova T. Yu. (1996) Systems of thermody-namically coordinated laws of conservation invariant under rotations. Siberian Math.J. Vol. 37.4.pp. 690–705. 1996.MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Mihailova T. Yu. (1997) Thermodynamically coordinated laws of conservation with unknowns of arbitrary weight. Siberian Math. J. Vol. 38. 3. 1997.MathSciNetGoogle Scholar
  5. 5.
    Godunov S. K. and Mihailova T. Yu. (1998) Representation of the Rotation Groups and Spherical Functions. Universitetskaya Seriya. Vol. 3. Scientific Books Publisher.Novosibirsk. 1998 [in Russian].Google Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • S. K. Godunov
    • 1
  1. 1.Sobolev Institute of MathematicsNovosibirskRussia

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