Implementation of standard penalty procedures for the solution of incompressible Navier–Stokes equations, employing the element-free Galerkin method

Abstract

The present work introduces an alternative implementation of the element-free Galerkin method (EFGM) for the steady incompressible Navier-Stokes equations. The linear momentum balance and mass conservation equations have been developed on the basis of this global weak formulation. The weak forms of both equations have been coupled by means of two standard penalty procedures, which have been previously formulated and successfully employed in mesh-based numerical techniques such as the finite element method (FEM). These include the consistent penalty method (CPM) and reduced integration penalty method (RIPM). A detailed explanation concerning the characteristics inherent to the implementation of both penalty procedures in the EFGM based solutions for the incompressible Navier-Stokes equations, has also been provided. The resulting systems of equations have been adapted to the solution of different well-known incompressible flow benchmark problems. The feasibility and reliability of extending the implementation of these penalty procedures to the EFGM based solutions has been verified by comparison with the numerical techniques proposed and the results reported by other researchers. Results have revealed that this technique could be successfully used in the solution of Newtonian incompressible flow problems under the aforementioned penalty approaches.