A mimetic finite difference discretization for the incompressible Navier–Stokes equations

2008 ◽  
Vol 56 (8) ◽  
pp. 1101-1106 ◽  
Author(s):  
A. Abbà ◽  
L. Bonaventura
Keyword(s):  
Finite Difference ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Finite Difference Discretization ◽  
Difference Discretization

Supercomputing of Supersonic Flows Using Upwind Relaxation and MacCormack Schemes

1988 ◽  
Vol 110 (1) ◽  
pp. 62-68 ◽  
Author(s):  
Oktay Baysal
Keyword(s):  
Stokes Equations ◽  
Supersonic Flows ◽  
Navier Stokes ◽  
Computational Algorithms ◽  
Navier Stokes Equations ◽  
Relaxation Scheme ◽  
Finite Volume Discretization ◽  
Finite Difference Discretization ◽  
The Mathematical Model ◽  
Difference Discretization

The impetus of this paper is the comparative applications of two numerical schemes for supersonic flows using computational algorithms tailored for a supercomputer. The mathematical model is the conservation form of Navier-Stokes equations with the effect of turbulence being modeled algebraically. The first scheme is an implicit, unfactored, upwind-biased, line-Gauss-Seidel relaxation scheme based on finite-volume discretization. The second scheme is the explicit-implicit MacCormack scheme based on finite-difference discretization. The best overall efficiences are obtained using the upwind relaxation scheme. The integrity of the solutions obtained for the example cases is shown by comparisons with experimental and other computational results.

Investigation of the stability of boundary layers by a finite-difference model of the Navier—Stokes equations

1976 ◽  
Vol 78 (2) ◽  
pp. 355-383 ◽  
Author(s):  
H. Fasel
Keyword(s):  
Finite Difference ◽  
Stability Theory ◽  
Stokes Equations ◽  
Time Dependent ◽  
Linear Stability Theory ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Navier Stokes Equations ◽  
The Stability ◽  
Small Periodic

The stability of incompressible boundary-layer flows on a semi-infinite flat plate and the growth of disturbances in such flows are investigated by numerical integration of the complete Navier–;Stokes equations for laminar two-dimensional flows. Forced time-dependent disturbances are introduced into the flow field and the reaction of the flow to such disturbances is studied by directly solving the Navier–Stokes equations using a finite-difference method. An implicit finitedifference scheme was developed for the calculation of the extremely unsteady flow fields which arose from the forced time-dependent disturbances. The problem of the numerical stability of the method called for special attention in order to avoid possible distortions of the results caused by the interaction of unstable numerical oscillations with physically meaningful perturbations. A demonstration of the suitability of the numerical method for the investigation of stability and the initial growth of disturbances is presented for small periodic perturbations. For this particular case the numerical results can be compared with linear stability theory and experimental measurements. In this paper a number of numerical calculations for small periodic disturbances are discussed in detail. The results are generally in fairly close agreement with linear stability theory or experimental measurements.

scholarly journals Fast solvers for finite difference approximations for the stokes and navier-stokes equations

1996 ◽  
Vol 38 (2) ◽  
pp. 274-290 ◽  
Author(s):  
Dongho Shin ◽  
John C. Strikwerda
Keyword(s):  
Finite Difference ◽  
Stokes Equations ◽  
Linear Equations ◽  
Computational Effort ◽  
Navier Stokes ◽  
Fast Solvers ◽  
Navier Stokes Equations ◽  
Finite Difference Approximations ◽  
Grid Points ◽  
First Time

AbstractWe consider several methods for solving the linear equations arising from finite difference discretizations of the Stokes equations. The two best methods, one presented here for the first time, apparently, and a second, presented by Bramble and Pasciak, are shown to have computational effort that grows slowly with the number of grid points. The methods work with second-order accurate discretizations. Computational results are shown for both the Stokes equations and incompressible Navier-Stokes equations at low Reynolds number.

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