Efficient resolution of incompressible Navier–Stokes equations using a robust high-order pseudo-spectral approach

Abstract

An accurate numerical tool is presented in this work to investigate the stationary incompressible Navier–Stokes equations. The proposed approach is based on a pseudo-spectral method for discretizing the differential equations and the asymptotic numerical method to convert nonlinear systems into linear algebraic equations. The coupling of the spectral method with the asymptotic numerical method is considered as an efficient algorithm to solve any nonlinear differential equations. Their efficiency and robustness are examined here on the flow fluid in different canal with different geometries. These computational efficiency and performance have been analysed via several numerical and benchmark examples of incompressible fluid flow in lid-driven cavity and vortex shedding over L-Shaped cavity and fluid flow around a square obstacle. The validation of the proposed approach is made by comparison between the obtained results and those calculated using a finite element method or Ansys commercial code. This validation asserts that the presented numerical tool can be promise for solving fluid flow problems with high accuracy.