scholarly journals A posteriori finite element bounds to linear functional outputs of the three-dimensional Navier-Stokes equations

2004 ◽  
Vol 61 (11) ◽  
pp. 1835-1859 ◽  
Author(s):  
Zhong Cheng ◽  
Marius Paraschivoiu
Keyword(s):  
Finite Element ◽  
Linear Functional ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
A Posteriori ◽  
Navier Stokes Equations

scholarly journals A convergent FV–FE scheme for the stationary compressible Navier–Stokes equations

2020 ◽  
Author(s):  
Charlotte Perrin ◽  
Khaled Saleh
Keyword(s):  
Finite Element ◽  
Numerical Scheme ◽  
Space Dimension ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Convergence Result ◽  
Ideal Gas ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Industrial Software

Abstract In this paper we prove a convergence result for a discretization of the three-dimensional stationary compressible Navier–Stokes equations assuming an ideal gas pressure law $p(\rho )=a \rho ^{\gamma }$ with $\gamma> \frac{3}{2}$. It is the first convergence result for a numerical method with adiabatic exponents $\gamma $ less than $3$ when the space dimension is 3. The considered numerical scheme combines finite volume techniques for the convection with the Crouzeix–Raviart finite element for the diffusion. A linearized version of the scheme is implemented in the industrial software CALIF3S developed by the French Institut de Radioprotection et de Sûreté Nucléaire.

A Finite Element Analysis of the Navier-Stokes Equations Applied to High Speed Thin Film Lubrication

1987 ◽  
Vol 109 (1) ◽  
pp. 71-76 ◽  
Author(s):  
J. O. Medwell ◽  
D. T. Gethin ◽  
C. Taylor
Keyword(s):  
Finite Element ◽  
High Speed ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
The Finite Element Method ◽  
Thin Film Lubrication ◽  
Element Analysis ◽  
Navier Stokes Equations ◽  
Film Lubrication

The performance of a cylindrical bore bearing fed by two axial grooves orthogonal to the load line is analyzed by solving the Navier-Stokes equations using the finite element method. This produces detailed information about the three-dimensional velocity and pressure field within the hydrodynamic film. It is also shown that the method may be applied to long bearing geometries where recirculatory flows occur and in which the governing equations are elliptic. As expected the analysis confirms that lubricant inertia does not affect bearing performance significantly.

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