A cell-based smoothed finite element method stabilized by implicit SUPG/SPGP/Fractional step method for incompressible flow

Abstract

In this paper, the exhaustive usage and implementation of Streamline-Upwind/Petrov-Galerkin method combining with Stabilized Pressure Gradient Projection (SUPG/SPGP) for incompressible Navier-Stokes equations are investigated. We validate and explore the behavior of cell-based smoothed finite element method (CS-FEM) and finite element method (FEM) based on SUPG/SPGP on five numerical examples. First, the Taylor-Green vortex example shows that CS-FEM based on SUPG/SPGP (CSFEM-SUPG/SPGP) are more accurate and has better robustness against distorted mesh than that of FEM based on SUPG/SPGP (FEM-SUPG/SPGP). Moreover, the wider range of SPGP stability parameter for CS-FEM-SUPG/SPGP is found in the condition of maintaining accurate result. Meanwhile, the lid-driven cavity flow example shows that the SUPG/SPGP method is favorable for incompressible flow at relatively high Reynolds number. The other numerical examples show good performances of the proposed method on the unsteady flows and micro-channel flow. In summary, proposed CS-FEM-SUPG/SPGP shows good performances on obtaining accurate results.