Semi-Analytical Pressure-Based Solution for Incompressible Navier-Stokes Equations
Daniel J. N. M. Chalhub1; Leandro A. Sphaier1; Leonardo S. de B. Alves1
1 Universidade Federal Fluminense
doi:10.20906/CPS/COB-2015-2105
Resumo
The present work developed a novel numerical method for solving the unsteady incompressible Navier-Stokes equations with primitive variables in two dimensions that can be easily extendable to three dimensions. The methodology is based on Projection Methods using a mixed approach through the Classical Integral Transform Technique (CITT). Knowing that the main bottleneck of the classical pressure-correction approach is the solution of the pressure Poisson equation (PPE), this work proposes a different approach using the classic Projection Method for advancing in time the Navier-Stokes equations and CITT to find pressure dependence on the discrete velocity field in a semi-analytical manner, using the previous time-step pressure field as a filter. For comparison purposes, the Finite Volume Method (FVM) was also used, where the PPE was solved with a Gauss-Seidel iterative procedure. Three methods were computed and compared: CITT using single transformation with filtering scheme (CITT-ST-F), CITT using single transformation without filtering scheme (CITT-ST) and Finite Volumes Methods with Gauss-Seidel solver (FVM). The obtained results were compared with the literature showing a very good agreement for both test cases. One could see that for coarse meshes, CITT-ST-F and FVM had similar performances. However for more refined meshes, CITT-ST-F overcame FVM performance.
Palavras-chave: Incompressible Navier-Stokes; Projection Methods; Integral Transforms; Incompressible Navier-Stokes