Solution of the Navier-Stokes equations by the spectral-difference method

1994 ◽  
Vol 10 (3) ◽  
pp. 345-368 ◽  
Author(s):  
Arturo B. Cortes ◽  
J. D. Miller
Keyword(s):  
Difference Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Spectral Difference ◽  
Navier Stokes Equations ◽  
Spectral Difference Method

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.

Differential Formulation of Discontinuous Galerkin and Related Methods for the Navier-Stokes Equations

2013 ◽  
Vol 13 (4) ◽  
pp. 1013-1044 ◽  
Author(s):  
Haiyang Gao ◽  
Z. J. Wang ◽  
H. T. Huynh
Keyword(s):  
Discontinuous Galerkin ◽  
Stokes Equations ◽  
High Order Accuracy ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Correction Procedure ◽  
Spectral Difference ◽  
Navier Stokes Equations ◽  
Differential Formulation ◽  
Continuous Scheme

AbstractA new approach to high-order accuracy for the numerical solution of conservation laws introduced by Huynh and extended to simplexes by Wang and Gao is renamed CPR (correction procedure or collocation penalty via reconstruction). The CPR approach employs the differential form of the equation and accounts for the jumps in flux values at the cell boundaries by a correction procedure. In addition to being simple and economical, it unifies several existing methods including discontinuous Galerkin, staggered grid, spectral volume, and spectral difference. To discretize the dif-fusion terms, we use the BR2 (Bassi and Rebay), interior penalty, compact DG (CDG), and I-continuous approaches. The first three of these approaches, originally derived using the integral formulation, were recast here in the CPR framework, whereas the I-continuous scheme, originally derived for a quadrilateral mesh, was extended to a triangular mesh. Fourier stability and accuracy analyses for these schemes on quadrilateral and triangular meshes are carried out. Finally, results for the Navier-Stokes equations are shown to compare the various schemes as well as to demonstrate the capability of the CPR approach.

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