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ABSTRACT
In the aspect of numerical methods for incompressible flow problems, there are two different algorithms: semi-implicit method for pressure-linked equations (SIMPLE) series algorithms and the pressure Poisson algorithm. This paper introduced a new discretized pressure Poisson algorithm for the steady incompressible flow based on a nonstaggered grid. Compared with the SIMPLE series algorithms, this paper did not introduce three correction variables. So, there is no need to implement the guess-and-correct procedure for the calculation of pressure and velocity. Compared with the pressure Poisson algorithm, there is no need to calculate unsteady Navier–Stokes equations for steady problems in the new discretized pressure Poisson algorithm. Meanwhile, as the finite volume method and cell-centered grid are used, the governing equation for pressure is obtained from the continuity equation and the boundary conditions for pressure are easily obtained. This new discretized pressure Poisson algorithm was tested at the lid-driven cavity flow problem on a nonstaggered grid and the results are also reliable.
Nomenclature
| h | = | grid spacing |
| Δt | = | time step |
| Re | = | Reynolds number |
| t | = | dimensionless time |
| x,y | = | dimensionless coordinates |
| u,v | = | dimensionless velocity components in x- and y-directions, respectively |
| = | pseudo-velocities | |
| p | = | dimensionless pressure |
| = | pseudo-pressure | |
| ψ | = | stream function |
| = | velocity and pressure corrections | |
| a,b | = | coefficients in discretized results |
| = | three residual variables for continuity and momentum equations | |
| = | three mean residuals for continuity and momentum equations | |
| = | residuals of momentum equations and pressure equation | |
| Subscripts | = | |
| w,e,s,n | = | quantity at points w,e,s,n |
| W,E,S,N,P | = | quantity at points W,E,S,N,P |
| nb | = | quantity at nearby points (w,e,s,n) |
| u,v,p | = | discretized velocity and pressure equations |
| Superscript | = | |
| n,n−1 | = | current and previous iterative steps respectively |
Nomenclature
| h | = | grid spacing |
| Δt | = | time step |
| Re | = | Reynolds number |
| t | = | dimensionless time |
| x,y | = | dimensionless coordinates |
| u,v | = | dimensionless velocity components in x- and y-directions, respectively |
| = | pseudo-velocities | |
| p | = | dimensionless pressure |
| = | pseudo-pressure | |
| ψ | = | stream function |
| = | velocity and pressure corrections | |
| a,b | = | coefficients in discretized results |
| = | three residual variables for continuity and momentum equations | |
| = | three mean residuals for continuity and momentum equations | |
| = | residuals of momentum equations and pressure equation | |
| Subscripts | = | |
| w,e,s,n | = | quantity at points w,e,s,n |
| W,E,S,N,P | = | quantity at points W,E,S,N,P |
| nb | = | quantity at nearby points (w,e,s,n) |
| u,v,p | = | discretized velocity and pressure equations |
| Superscript | = | |
| n,n−1 | = | current and previous iterative steps respectively |
Acknowledgments
This work was supported by International Program for Ph.D. Candidates of Sun Yat-sen University, and by funds from Guangdong Provincial Scientific and Technological Project (Nos. 2013B090800008 and 2014B030301034). Finally, we also express our appreciation to the support of University of Wollongong.