Abstract
In this paper, the variational principles of hydrodynamic problems for the incompressible and compressible viscous fluids are established. These principles are principles of maximum power losses. Their generalized variational principles are also discussed on the basis of Lagrangian multiplier methods.
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References
Lin,C.C. and L.Rubinov, On the flow behind curved shocks, Journal of Mathematics and Physics, Vol. 27, (1948), 105–129.
Skobeikin,V.I., Variational principles in hydrodynamics, Soviet Physics JETP, Vol. 4, No. 1, (1957), 68–71.
Guderley,K.G., An extremum principle for three-dimensional compressible inviscid flows, SIAM, Journal of Applied Mathematics, Vol. 23, No. 2, (1972), 259–275.
Morice,P., Un Principe Variational et ume Méthode de Résolution Numérique par Elements Finis pour des Ecoulements Avec Frontiers Libres, Paper presented at XIII Symposium of Dynamics of Fluids, Kortawo, Poland, Sept. (1977).
Manwell,A.R., A variational principle for steady Honenergie compressible flow with finite shocks, Wave Motion, Vol. 2, (1980), 83–95.
Hafez,M. and D.Lovell, Numerical solution of transonic stream function equation, AIAA Journal, Vol. 21, No. 3, (1983).
Chien,W.Z., Method of high-order Lagrange multiplier and generalized variational principles of elasticity with more general forms of functionals, Applied Mathematics and Mechanics, Vol. 4, No. 2, (1983), 143–157.
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Wei-zang, C. Variational principles and generalized variational principles in hydrodynamics of viscous fluids. Appl Math Mech 5, 1281–1296 (1984). https://doi.org/10.1007/BF01904951
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DOI: https://doi.org/10.1007/BF01904951