Integral Transform Analysis of Poisson Problems that Occur in Discrete Solutions of the Incompressible Navier-Stokes Equations

The present work presents an alternate method for solving the poisson equation for calculating the pressure field that appears in many discrete numerical solvers of the incompressible Navier-Stokes equations. The methodology is based on a pressure-correction scheme with a mixed approach that employs...

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Bibliographic Details
Published in:Journal of physics. Conference series 2014-01, Vol.547 (1), p.12040-10
Main Authors: Chalhub, Daniel J N M, Sphaier, Leandro A, Alves, Leonardo S de B
Format: Article
Language:English
Subjects:
Convergence
Error analysis
Flow control
Fluid flow
Integral transforms
Integrals
Mathematical analysis
Mathematical models
Navier-Stokes equations
Physics
Poisson equation
Transformations
Transforms
Velocity distribution
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Summary:The present work presents an alternate method for solving the poisson equation for calculating the pressure field that appears in many discrete numerical solvers of the incompressible Navier-Stokes equations. The methodology is based on a pressure-correction scheme with a mixed approach that employs Integral Transform Technique for the calculation of the pressure field from a given discrete velocity field. Two solution schemes are analyzed, these being the single transformation and the double transformation. The poisson equation is solved with the two different schemes using a prescribed source term to simulate the discrete data that could arise in the solution process of the momentum equation and an numerical results are presented. An error analysis of these results show that the single-transformation scheme is computationally superior to the double transformation, and that good convergence rates can be obtained with few terms in the series. Moreover, it was also verified that the series solution employed for the Poisson equation maintains the original spatial order of the discretization.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/547/1/012040