Navier-Stokes-Fourier Equations: A Rational Asymptotic by Radyadour Kh. Zeytounian

By Radyadour Kh. Zeytounian

This study monograph bargains with a modeling concept of the process of Navier-Stokes-Fourier equations for a Newtonian fluid governing a compressible viscous and warmth accomplishing flows. the most target is threefold. First , to 'deconstruct' this Navier-Stokes-Fourier approach with a purpose to unify the puzzle of some of the partial simplified approximate versions utilized in Newtonian Classical Fluid Dynamics and this, first side, have evidently a not easy process and an important pedagogic effect at the collage schooling.

The moment side of the most aim is to stipulate a rational constant asymptotic/mathematical concept of the of fluid flows modeling at the foundation of a customary Navier-Stokes-Fourier preliminary and boundary price challenge. The 3rd aspect is dedicated to a demonstration of our rational asymptotic/mathematical modeling thought for numerous technological and geophysical stiff difficulties from: aerodynamics, thermal and thermocapillary convections and in addition meteofluid dynamics.

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Extra resources for Navier-Stokes-Fourier Equations: A Rational Asymptotic Modelling Point of View

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Obviously, this result is in sharp contrast with experience! For instance, an aircraft could not fly. Suppose that, initially, the aircraft and the fluid (air) are both at rest, then the aircraft begins to move. Since vorticity cannot be produced (Lagrange – permanence of irrotational flow), the potential flow around the aircraft cannot produce any lift, so that flight is impossible. Such a paradox can be avoided if vorticity is present. However, the problem remains of understanding how vorticity can be created in the system.

4. Characteristic of the discipline of gas dynamics is the postulate that the thermodynamic pressure, introduced via functional relations among the state variables (see Sect. 3), is equal to this dynamical pressure. When the deformation D(u) ¼ 0, for a perfect fluid, p is the thermodynamic pressure when the fluid is compressible, while p is simply an independent dynamical variable otherwise. For an incompressible perfect or viscous fluid (Navier, see Sect. 2) p is not an unknown quantity, because it can be determined when we have found the velocity field u.

Concerning the boundary conditions (kinematic and dynamic) for this free surface problem, see the next Sect. ) For meteorological motions (considered in the Chap. 9), when we consider various approximate model equations – f -plane equations, primitive equations, quasi-geostrophic equations, or Boussinesq equations – it is necessary, in fact (mainly because the filtering acoustic waves), to resolve associated unsteady adjustment problems for the formulation of consistent initial conditions for these simplified model equations.

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