Numerical analysis of the Taylor Galerkin Pressure Correction (TGPC) finite element method for Newtonian fluid

Abstract

In this study, a time stepping Taylor Galerkin Pressure Correction finite element scheme (TGPC) is investigated on the basis of incompressible Newtonian flows. Naiver-Stoke partial differential equations have been used to describe the motion of the fluid. The equations consist of a time-dependent continuity equation for conservation of mass and time-dependent conservation of momentum equations. Examples considered include a start-up of Poiseuille flow in a rectangular channel for the Newtonian fluid. In that context, three different meshes 2×2, 5×5 and 10×10 are implemented to investigate the effect mesh refinements on the accuracy of the solution. In addition, the behaviour of velocity and pressure are reported in this study.

Keywords: Finite element methods, Taylor expansion, Naiver-Stoke equations, Newtonian fluid, Galerkin method