Computation of Incompressible Three-Dimensional Mixed Convection Flows in Long Aspect Ratio Channels Using an Efficient Finite Difference Method for Vectorial Supercomputers

2005 ◽  
Author(s):  
Xavier Nicolas ◽  
Shihe Xin
Keyword(s):  
Finite Difference ◽  
Aspect Ratio ◽  
Finite Difference Method ◽  
Mixed Convection ◽  
Spectral Decomposition ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Factorization Method ◽  
Navier Stokes ◽  
Navier Stokes Equations

Based on Goda’s algorithm and second-order central finite differences, a very efficient vectorized code is tailored to solve 3D incompressible Navier-Stokes equations for mixed convection flows in high streamwise aspect ratio channels. The code takes advantage of incremental factorization method of ADI type, spectral decomposition of the ID Laplace operators and TDMA algorithm. It is validated through experiments of various Poiseuille-Rayleigh-Be´nard flows with steady longitudinal and unsteady transverse rolls.

scholarly journals Calculating Rotordynamic Coefficients of Seals by Finite-Difference Techniques

1987 ◽  
Vol 109 (3) ◽  
pp. 388-394 ◽  
Author(s):  
F. J. Dietzen ◽  
R. Nordmann
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Flow Field ◽  
Pressure Distribution ◽  
Difference Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Rotordynamic Coefficients ◽  
Finite Difference Techniques

For modelling the turbulent flow in a seal the Navier-Stokes equations in connection with a turbulence model (k-ε-model) are solved by a finite-difference method. A motion of the shaft around the centered position is assumed. After calculating the corresponding flow field and the pressure distribution, the rotordynamic coefficients of the seal can be determined. These coefficients are compared with results obtained by using the bulk flow theory of Childs [1] and with experimental results.

A Semi-Staggered Numerical Procedure for the Incompressible Navier-Stokes Equations on Curvilinear Grids

2011 ◽  
Author(s):  
Hessam Babaee ◽  
Sumanta Acharya
Keyword(s):  
Finite Difference ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Second Order ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Benchmark Problems ◽  
Navier Stokes Equations ◽  
Curvilinear Grids

An accurate and efficient finite difference method for solving the three dimensional incompressible Navier-Stokes equations on curvilinear grids is developed. The semi-staggered grid layout has been used in which all three components of velocity are stored on the corner vertices of the cell facilitating a consistent discretization of the momentum equations as the boundaries are approached. Pressure is stored at the cell-center, resulting in the exact satisfaction the discrete continuity. The diffusive terms are discretized using a second-order central finite difference. A third-order biased upwind scheme is used to discretize the convective terms. The momentum equations are integrated in time using a semi-implicit fractional step methodology. The convective and diffusive terms are advanced in time using the second-order Adams-Bashforth method and Crank-Nicolson method respectively. The Pressure-Poisson is discretized in a similar approach to the staggered gird layout and thus leading to the elimination of the spurious pressure eigen-modes. The validity of the method is demonstrated by two standard benchmark problems. The flow in driven cavity is used to show the second-order spatial convergence on an intentionally distorted grid. Finally, the results for flow past a cylinder for several Reynolds numbers in the range of 50–150 are compared with the existing experimental data in the literature.

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