Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Unsteady perturbed flow at low Mach number of a viscous compressible fluid


Author: Carlo Ferrari
Journal: Quart. Appl. Math. 55 (1997), 157-165
MSC: Primary 76N10
DOI: https://doi.org/10.1090/qam/1433759
MathSciNet review: MR1433759
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Abstract: The problem of the unsteady perturbed two-dimensional flow at low Mach number of a viscous compressible fluid is studied taking the relation between the stress and deformation rates tensors that was obtained and applied in [1] and [3]. It is shown that the system of equations describing the phenomenon is totally hyperbolic and therefore the perturbations in any point $ P$ of the field are propagated by means of waves corresponding to four characteristic surfaces passing through $ P$. The displacement and propagation velocities of these waves are determined as well as their dependence on the orientation of their front in $ P$; it is shown besides that the discontinuity vector across the waves has components both longitudinal and transversal. The variation laws of the fluid velocities both on the characteristic surfaces and along their bicharacteristics are determined, which allows us to solve the Cauchy problem with a ``step-by-step'' method.


References [Enhancements On Off] (What's this?)

  • [1] C. Ferrari, On the propagation of small perturbations in viscous compressible fluid, Acta Mech. [Suppl.] 3, 1-16 (1992)
  • [2] C. Cattaneo, Sulla conduzione del colore, Seminario matematico e fisico, Università di Modena, Società Tipografica Modenese, 1948
  • [3] C. Ferrari, The effect of the thermal conductivity on the propagation of small perturbations in viscous compressible fluid, Acta Mech. [Suppl.] 4, 305-311 (1994)
  • [4] T. Levi-Civita, Caracteristiques des Systémes Differentiels et Propagation des Ondes, Paris Libraries Felix Akan, 1932, pp. 56-61

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DOI: https://doi.org/10.1090/qam/1433759
Article copyright: © Copyright 1997 American Mathematical Society


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