Semi-Analytical Method for the Solution of the Poisson Equation Derived From the Navier-Stokes Using Integral Transforms

The present work proposes two methodologies using the Integral Transform Technique to solve the Poisson equation arising from the incompressible Navier-Stokes equations. The solution of this Poisson equation is very common in the formulations based on pressure-correction and are the main bottleneck of these approaches. The new formulation proposed in this work will allow the elimination of the pressure-velocity decomposition and also eliminate the sub-iterations of the usual pressure-correction methods. The results show a comparison in performance of both proposed approaches.