In this short chapter, the Navier-Stokes equations governing the motion of a viscous incompressible fluid are recalled. Two formulations are considered: the velocity-pressure formulation (also called “primitive variables” formulation) and the vorticity-streamfunction formulation. The formulation using vor...
This chapter is concerned with the finite-element approximation of viscous, incompressible, laminar flows. The governing partial differential equations are the continuity equation and the Navier–Stokes equations. The first of these is the mathematical realization of the incompressibility of the flow. ...
The Navier–Stokes equations for an incompressible fluid [1]∂ui∂t=−∂uiuj∂xj+Xi−1ρ∂p∂xi+v∂2ui∂xj2 form the basis for an LES of the PBL, where ui satisfy the continuity equation: [2]∂ui∂xi=0 In eqns [1] and [2], ui are flow velocities in the...
Tags Compressible Fluid Navier-stokes In summary: Interesting. The Boussinesq approximation says that if you know the density of the fluid and the compressibility of the fluid, you can approximate the pressure and velocity by solving the equation for ##\vec{p}## and ##\vec{v}##. Jun 29,...
turbulence models (such as the k-ε model), are used in practical computational fluid dynamics (CFD) applications when modeling turbulent flows. Another technique for solving numerically the Navier–Stokes equation is the Large-eddy simulation (LES). This approach is computationally more expensive tha...
WILLIAMS P T,BAKER A J.Incompressible computational fluid dynamics and the continuity constraint methods for the three-dimensional Navier-Stokes equations. Numerical Heat Transfer:Part B . 1996P.T. Williams, A.J. Baker, Incompressible computational fluid dynamics and the continuity constraint method ...
We consider the equations which describe the motion of a viscous compressible fluid, taking into consideration the case of inflow and/or outflow through the boundary. By means of some a priori estimates we prove the existence of a global (in time) solution. Moreover, as a consequence of a...
The governing equations consist of the stationary Navier–Stokes equations describing the compressible fluid flows and the stationary Cahn–Hilliard-type diffuse equation for the mass concentration difference. We prove the existence of weak solutions when the adiabatic exponent γ satisfies γ>43. The ...
For an incompressible fluid, the pressure in the Navier Stokes equation represents the isotropic part of the stress tensor. It is determined up to an arbitrary constant value; that is, adding an arbitrary constant to the pressure at all location throughout the flow field still enables...
In the context of fluid mechanics, the concept of relative entropies has proven successful in ruling out the aforementioned examples of non-uniqueness; energy-dissipating weak solutions e. g. to the incompressible Navier–Stokes equation are subject to a weak–strong uniqueness principle [75,81,93...