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

32nd UIT (Italian Union of Thermo–fluid-dynamics) Heat Transfer Conference

物理学;力学

Chalhub, Daniel J. N. M.^1 ; Sphaier, Leandro A.^1 ; Alves, Leonardo S. De B.^1

Laboratory of Theoretical and Applied Mechanics, LMTA Department of Mechanical Engineering-TEM/PGMEC, Universidade Federal Fluminense, Niterói, Rio de Janeiro, Brazil^1

关键词: Incompressible Navier Stokes equations;    Integral transform;    Integral transform technique;    Momentum equation;    Numerical results;    Numerical solvers;    Pressure correction;    Transformation scheme;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/547/1/012040/pdf
DOI  :  10.1088/1742-6596/547/1/012040

学科分类：力学，机械学

来源: IOP

【 摘 要 】

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.