A comparison of numerical solutions based on two different rates of deformation tensors by using the artificial compressibility method

Abstract

In this paper, the Newtonian incompressible Navier-Stokes equations in cylindrical polar coordinates can be solved using a Galerkin finite element method proposed based on an artificial compressibility scheme. In this study, two various formulations of the viscous stress tensor are represented, named the rate of deformation tensor T_rd  and the velocity gradient tensor T_gv. A comparison is undertaken between both options T_rd  and T_gv. In this context, attention is paid to the rate of convergence and the influence of variation in Reynolds number (Re) and artificial compressible parameter β_ac  by using both assumptions, T_rd  and T_gv. The critical values of Reynolds number (Re) and artificial compressible parameter β_ac  are highlighted in this study as well. Generally, through the analysis of results, we detected that the results with the rate of deformation tensor T_rd  are better than the results with the velocity gradient tensor T_gv.